├── LICENSE ├── README.md ├── ffttest.xcodeproj ├── project.pbxproj ├── project.xcworkspace │ ├── contents.xcworkspacedata │ └── xcuserdata │ │ └── christopher.xcuserdatad │ │ └── UserInterfaceState.xcuserstate └── xcuserdata │ └── christopher.xcuserdatad │ ├── xcdebugger │ └── Breakpoints_v2.xcbkptlist │ └── xcschemes │ ├── ffttest.xcscheme │ └── xcschememanagement.plist └── ffttest ├── fft.swift └── main.swift /LICENSE: -------------------------------------------------------------------------------- 1 | CC0 1.0 Universal 2 | 3 | Statement of Purpose 4 | 5 | The laws of most jurisdictions throughout the world automatically confer 6 | exclusive Copyright and Related Rights (defined below) upon the creator and 7 | subsequent owner(s) (each and all, an "owner") of an original work of 8 | authorship and/or a database (each, a "Work"). 9 | 10 | Certain owners wish to permanently relinquish those rights to a Work for the 11 | purpose of contributing to a commons of creative, cultural and scientific 12 | works ("Commons") that the public can reliably and without fear of later 13 | claims of infringement build upon, modify, incorporate in other works, reuse 14 | and redistribute as freely as possible in any form whatsoever and for any 15 | purposes, including without limitation commercial purposes. These owners may 16 | contribute to the Commons to promote the ideal of a free culture and the 17 | further production of creative, cultural and scientific works, or to gain 18 | reputation or greater distribution for their Work in part through the use and 19 | efforts of others. 20 | 21 | For these and/or other purposes and motivations, and without any expectation 22 | of additional consideration or compensation, the person associating CC0 with a 23 | Work (the "Affirmer"), to the extent that he or she is an owner of Copyright 24 | and Related Rights in the Work, voluntarily elects to apply CC0 to the Work 25 | and publicly distribute the Work under its terms, with knowledge of his or her 26 | Copyright and Related Rights in the Work and the meaning and intended legal 27 | effect of CC0 on those rights. 28 | 29 | 1. Copyright and Related Rights. A Work made available under CC0 may be 30 | protected by copyright and related or neighboring rights ("Copyright and 31 | Related Rights"). Copyright and Related Rights include, but are not limited 32 | to, the following: 33 | 34 | i. the right to reproduce, adapt, distribute, perform, display, communicate, 35 | and translate a Work; 36 | 37 | ii. moral rights retained by the original author(s) and/or performer(s); 38 | 39 | iii. publicity and privacy rights pertaining to a person's image or likeness 40 | depicted in a Work; 41 | 42 | iv. rights protecting against unfair competition in regards to a Work, 43 | subject to the limitations in paragraph 4(a), below; 44 | 45 | v. rights protecting the extraction, dissemination, use and reuse of data in 46 | a Work; 47 | 48 | vi. database rights (such as those arising under Directive 96/9/EC of the 49 | European Parliament and of the Council of 11 March 1996 on the legal 50 | protection of databases, and under any national implementation thereof, 51 | including any amended or successor version of such directive); and 52 | 53 | vii. other similar, equivalent or corresponding rights throughout the world 54 | based on applicable law or treaty, and any national implementations thereof. 55 | 56 | 2. Waiver. To the greatest extent permitted by, but not in contravention of, 57 | applicable law, Affirmer hereby overtly, fully, permanently, irrevocably and 58 | unconditionally waives, abandons, and surrenders all of Affirmer's Copyright 59 | and Related Rights and associated claims and causes of action, whether now 60 | known or unknown (including existing as well as future claims and causes of 61 | action), in the Work (i) in all territories worldwide, (ii) for the maximum 62 | duration provided by applicable law or treaty (including future time 63 | extensions), (iii) in any current or future medium and for any number of 64 | copies, and (iv) for any purpose whatsoever, including without limitation 65 | commercial, advertising or promotional purposes (the "Waiver"). Affirmer makes 66 | the Waiver for the benefit of each member of the public at large and to the 67 | detriment of Affirmer's heirs and successors, fully intending that such Waiver 68 | shall not be subject to revocation, rescission, cancellation, termination, or 69 | any other legal or equitable action to disrupt the quiet enjoyment of the Work 70 | by the public as contemplated by Affirmer's express Statement of Purpose. 71 | 72 | 3. Public License Fallback. Should any part of the Waiver for any reason be 73 | judged legally invalid or ineffective under applicable law, then the Waiver 74 | shall be preserved to the maximum extent permitted taking into account 75 | Affirmer's express Statement of Purpose. In addition, to the extent the Waiver 76 | is so judged Affirmer hereby grants to each affected person a royalty-free, 77 | non transferable, non sublicensable, non exclusive, irrevocable and 78 | unconditional license to exercise Affirmer's Copyright and Related Rights in 79 | the Work (i) in all territories worldwide, (ii) for the maximum duration 80 | provided by applicable law or treaty (including future time extensions), (iii) 81 | in any current or future medium and for any number of copies, and (iv) for any 82 | purpose whatsoever, including without limitation commercial, advertising or 83 | promotional purposes (the "License"). The License shall be deemed effective as 84 | of the date CC0 was applied by Affirmer to the Work. Should any part of the 85 | License for any reason be judged legally invalid or ineffective under 86 | applicable law, such partial invalidity or ineffectiveness shall not 87 | invalidate the remainder of the License, and in such case Affirmer hereby 88 | affirms that he or she will not (i) exercise any of his or her remaining 89 | Copyright and Related Rights in the Work or (ii) assert any associated claims 90 | and causes of action with respect to the Work, in either case contrary to 91 | Affirmer's express Statement of Purpose. 92 | 93 | 4. Limitations and Disclaimers. 94 | 95 | a. No trademark or patent rights held by Affirmer are waived, abandoned, 96 | surrendered, licensed or otherwise affected by this document. 97 | 98 | b. Affirmer offers the Work as-is and makes no representations or warranties 99 | of any kind concerning the Work, express, implied, statutory or otherwise, 100 | including without limitation warranties of title, merchantability, fitness 101 | for a particular purpose, non infringement, or the absence of latent or 102 | other defects, accuracy, or the present or absence of errors, whether or not 103 | discoverable, all to the greatest extent permissible under applicable law. 104 | 105 | c. Affirmer disclaims responsibility for clearing rights of other persons 106 | that may apply to the Work or any use thereof, including without limitation 107 | any person's Copyright and Related Rights in the Work. Further, Affirmer 108 | disclaims responsibility for obtaining any necessary consents, permissions 109 | or other rights required for any use of the Work. 110 | 111 | d. Affirmer understands and acknowledges that Creative Commons is not a 112 | party to this document and has no duty or obligation with respect to this 113 | CC0 or use of the Work. 114 | 115 | For more information, please see 116 | 117 | 118 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Swift-FFT-Example 2 | 3 | Example Usage of the Fourier-Transform using Apple's Accelerate Framework in Swift, including a Bandpass Filter. This is more intendended as an example on how to use both forward and backward FFT, and how to apply a bandpass filter inbetween these steps. Evenly sampled values are assumed with an underlying framerate (i.e. FPS) for the bandpass filter to work. Both phase and magnitudes are calculated and bandpassed, as well as the values themselves. 4 | 5 | ## Compatibility 6 | 7 | Tested with Swift 3 and Xcode 8.3.1. 8 | -------------------------------------------------------------------------------- /ffttest.xcodeproj/project.pbxproj: -------------------------------------------------------------------------------- 1 | // !$*UTF8*$! 2 | { 3 | archiveVersion = 1; 4 | classes = { 5 | }; 6 | objectVersion = 46; 7 | objects = { 8 | 9 | /* Begin PBXBuildFile section */ 10 | 9D149E491B82226B00FF68B2 /* main.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9D149E481B82226B00FF68B2 /* main.swift */; }; 11 | 9D149E501B8222B100FF68B2 /* fft.swift in Sources */ = {isa = PBXBuildFile; fileRef = 9D149E4F1B8222B100FF68B2 /* fft.swift */; }; 12 | /* End PBXBuildFile section */ 13 | 14 | /* Begin PBXCopyFilesBuildPhase section */ 15 | 9D149E431B82226B00FF68B2 /* CopyFiles */ = { 16 | isa = PBXCopyFilesBuildPhase; 17 | buildActionMask = 2147483647; 18 | dstPath = /usr/share/man/man1/; 19 | dstSubfolderSpec = 0; 20 | files = ( 21 | ); 22 | runOnlyForDeploymentPostprocessing = 1; 23 | }; 24 | /* End PBXCopyFilesBuildPhase section */ 25 | 26 | /* Begin PBXFileReference section */ 27 | 9D149E451B82226B00FF68B2 /* ffttest */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; includeInIndex = 0; path = ffttest; sourceTree = BUILT_PRODUCTS_DIR; }; 28 | 9D149E481B82226B00FF68B2 /* main.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = main.swift; sourceTree = ""; }; 29 | 9D149E4F1B8222B100FF68B2 /* fft.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = fft.swift; sourceTree = ""; }; 30 | /* End PBXFileReference section */ 31 | 32 | /* Begin PBXFrameworksBuildPhase section */ 33 | 9D149E421B82226B00FF68B2 /* Frameworks */ = { 34 | isa = PBXFrameworksBuildPhase; 35 | buildActionMask = 2147483647; 36 | files = ( 37 | ); 38 | runOnlyForDeploymentPostprocessing = 0; 39 | }; 40 | /* End PBXFrameworksBuildPhase section */ 41 | 42 | /* Begin PBXGroup section */ 43 | 9D149E3C1B82226B00FF68B2 = { 44 | isa = PBXGroup; 45 | children = ( 46 | 9D149E471B82226B00FF68B2 /* ffttest */, 47 | 9D149E461B82226B00FF68B2 /* Products */, 48 | ); 49 | sourceTree = ""; 50 | }; 51 | 9D149E461B82226B00FF68B2 /* Products */ = { 52 | isa = PBXGroup; 53 | children = ( 54 | 9D149E451B82226B00FF68B2 /* ffttest */, 55 | ); 56 | name = Products; 57 | sourceTree = ""; 58 | }; 59 | 9D149E471B82226B00FF68B2 /* ffttest */ = { 60 | isa = PBXGroup; 61 | children = ( 62 | 9D149E481B82226B00FF68B2 /* main.swift */, 63 | 9D149E4F1B8222B100FF68B2 /* fft.swift */, 64 | ); 65 | path = ffttest; 66 | sourceTree = ""; 67 | }; 68 | /* End PBXGroup section */ 69 | 70 | /* Begin PBXNativeTarget section */ 71 | 9D149E441B82226B00FF68B2 /* ffttest */ = { 72 | isa = PBXNativeTarget; 73 | buildConfigurationList = 9D149E4C1B82226B00FF68B2 /* Build configuration list for PBXNativeTarget "ffttest" */; 74 | buildPhases = ( 75 | 9D149E411B82226B00FF68B2 /* Sources */, 76 | 9D149E421B82226B00FF68B2 /* Frameworks */, 77 | 9D149E431B82226B00FF68B2 /* CopyFiles */, 78 | ); 79 | buildRules = ( 80 | ); 81 | dependencies = ( 82 | ); 83 | name = ffttest; 84 | productName = ffttest; 85 | productReference = 9D149E451B82226B00FF68B2 /* ffttest */; 86 | productType = "com.apple.product-type.tool"; 87 | }; 88 | /* End PBXNativeTarget section */ 89 | 90 | /* Begin PBXProject section */ 91 | 9D149E3D1B82226B00FF68B2 /* Project object */ = { 92 | isa = PBXProject; 93 | attributes = { 94 | LastUpgradeCheck = 0830; 95 | ORGANIZATIONNAME = "Christopher Helf"; 96 | TargetAttributes = { 97 | 9D149E441B82226B00FF68B2 = { 98 | CreatedOnToolsVersion = 6.4; 99 | LastSwiftMigration = 0830; 100 | }; 101 | }; 102 | }; 103 | buildConfigurationList = 9D149E401B82226B00FF68B2 /* Build configuration list for PBXProject "ffttest" */; 104 | compatibilityVersion = "Xcode 5.2"; 105 | developmentRegion = English; 106 | hasScannedForEncodings = 0; 107 | knownRegions = ( 108 | en, 109 | ); 110 | mainGroup = 9D149E3C1B82226B00FF68B2; 111 | productRefGroup = 9D149E461B82226B00FF68B2 /* Products */; 112 | projectDirPath = ""; 113 | projectRoot = ""; 114 | targets = ( 115 | 9D149E441B82226B00FF68B2 /* ffttest */, 116 | ); 117 | }; 118 | /* End PBXProject section */ 119 | 120 | /* Begin PBXSourcesBuildPhase section */ 121 | 9D149E411B82226B00FF68B2 /* Sources */ = { 122 | isa = PBXSourcesBuildPhase; 123 | buildActionMask = 2147483647; 124 | files = ( 125 | 9D149E501B8222B100FF68B2 /* fft.swift in Sources */, 126 | 9D149E491B82226B00FF68B2 /* main.swift in Sources */, 127 | ); 128 | runOnlyForDeploymentPostprocessing = 0; 129 | }; 130 | /* End PBXSourcesBuildPhase section */ 131 | 132 | /* Begin XCBuildConfiguration section */ 133 | 9D149E4A1B82226B00FF68B2 /* Debug */ = { 134 | isa = XCBuildConfiguration; 135 | buildSettings = { 136 | ALWAYS_SEARCH_USER_PATHS = NO; 137 | CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x"; 138 | CLANG_CXX_LIBRARY = "libc++"; 139 | CLANG_ENABLE_MODULES = YES; 140 | CLANG_ENABLE_OBJC_ARC = YES; 141 | CLANG_WARN_BOOL_CONVERSION = YES; 142 | CLANG_WARN_CONSTANT_CONVERSION = YES; 143 | CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR; 144 | CLANG_WARN_EMPTY_BODY = YES; 145 | CLANG_WARN_ENUM_CONVERSION = YES; 146 | CLANG_WARN_INFINITE_RECURSION = YES; 147 | CLANG_WARN_INT_CONVERSION = YES; 148 | CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR; 149 | CLANG_WARN_SUSPICIOUS_MOVE = YES; 150 | CLANG_WARN_UNREACHABLE_CODE = YES; 151 | CLANG_WARN__DUPLICATE_METHOD_MATCH = YES; 152 | COPY_PHASE_STRIP = NO; 153 | DEBUG_INFORMATION_FORMAT = dwarf; 154 | ENABLE_STRICT_OBJC_MSGSEND = YES; 155 | ENABLE_TESTABILITY = YES; 156 | GCC_C_LANGUAGE_STANDARD = gnu99; 157 | GCC_DYNAMIC_NO_PIC = NO; 158 | GCC_NO_COMMON_BLOCKS = YES; 159 | GCC_OPTIMIZATION_LEVEL = 0; 160 | GCC_PREPROCESSOR_DEFINITIONS = ( 161 | "DEBUG=1", 162 | "$(inherited)", 163 | ); 164 | GCC_SYMBOLS_PRIVATE_EXTERN = NO; 165 | GCC_WARN_64_TO_32_BIT_CONVERSION = YES; 166 | GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR; 167 | GCC_WARN_UNDECLARED_SELECTOR = YES; 168 | GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE; 169 | GCC_WARN_UNUSED_FUNCTION = YES; 170 | GCC_WARN_UNUSED_VARIABLE = YES; 171 | MACOSX_DEPLOYMENT_TARGET = 10.12; 172 | MTL_ENABLE_DEBUG_INFO = YES; 173 | ONLY_ACTIVE_ARCH = YES; 174 | SDKROOT = macosx; 175 | SWIFT_OPTIMIZATION_LEVEL = "-Onone"; 176 | }; 177 | name = Debug; 178 | }; 179 | 9D149E4B1B82226B00FF68B2 /* Release */ = { 180 | isa = XCBuildConfiguration; 181 | buildSettings = { 182 | ALWAYS_SEARCH_USER_PATHS = NO; 183 | CLANG_CXX_LANGUAGE_STANDARD = "gnu++0x"; 184 | CLANG_CXX_LIBRARY = "libc++"; 185 | CLANG_ENABLE_MODULES = YES; 186 | CLANG_ENABLE_OBJC_ARC = YES; 187 | CLANG_WARN_BOOL_CONVERSION = YES; 188 | CLANG_WARN_CONSTANT_CONVERSION = YES; 189 | CLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR; 190 | CLANG_WARN_EMPTY_BODY = YES; 191 | CLANG_WARN_ENUM_CONVERSION = YES; 192 | CLANG_WARN_INFINITE_RECURSION = YES; 193 | CLANG_WARN_INT_CONVERSION = YES; 194 | CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR; 195 | CLANG_WARN_SUSPICIOUS_MOVE = YES; 196 | CLANG_WARN_UNREACHABLE_CODE = YES; 197 | CLANG_WARN__DUPLICATE_METHOD_MATCH = YES; 198 | COPY_PHASE_STRIP = NO; 199 | DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym"; 200 | ENABLE_NS_ASSERTIONS = NO; 201 | ENABLE_STRICT_OBJC_MSGSEND = YES; 202 | GCC_C_LANGUAGE_STANDARD = gnu99; 203 | GCC_NO_COMMON_BLOCKS = YES; 204 | GCC_WARN_64_TO_32_BIT_CONVERSION = YES; 205 | GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR; 206 | GCC_WARN_UNDECLARED_SELECTOR = YES; 207 | GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE; 208 | GCC_WARN_UNUSED_FUNCTION = YES; 209 | GCC_WARN_UNUSED_VARIABLE = YES; 210 | MACOSX_DEPLOYMENT_TARGET = 10.12; 211 | MTL_ENABLE_DEBUG_INFO = NO; 212 | SDKROOT = macosx; 213 | SWIFT_OPTIMIZATION_LEVEL = "-Owholemodule"; 214 | }; 215 | name = Release; 216 | }; 217 | 9D149E4D1B82226B00FF68B2 /* Debug */ = { 218 | isa = XCBuildConfiguration; 219 | buildSettings = { 220 | PRODUCT_NAME = "$(TARGET_NAME)"; 221 | SWIFT_VERSION = 5.2; 222 | }; 223 | name = Debug; 224 | }; 225 | 9D149E4E1B82226B00FF68B2 /* Release */ = { 226 | isa = XCBuildConfiguration; 227 | buildSettings = { 228 | PRODUCT_NAME = "$(TARGET_NAME)"; 229 | SWIFT_VERSION = 5.2; 230 | }; 231 | name = Release; 232 | }; 233 | /* End XCBuildConfiguration section */ 234 | 235 | /* Begin XCConfigurationList section */ 236 | 9D149E401B82226B00FF68B2 /* Build configuration list for PBXProject "ffttest" */ = { 237 | isa = XCConfigurationList; 238 | buildConfigurations = ( 239 | 9D149E4A1B82226B00FF68B2 /* Debug */, 240 | 9D149E4B1B82226B00FF68B2 /* Release */, 241 | ); 242 | defaultConfigurationIsVisible = 0; 243 | defaultConfigurationName = Release; 244 | }; 245 | 9D149E4C1B82226B00FF68B2 /* Build configuration list for PBXNativeTarget "ffttest" */ = { 246 | isa = XCConfigurationList; 247 | buildConfigurations = ( 248 | 9D149E4D1B82226B00FF68B2 /* Debug */, 249 | 9D149E4E1B82226B00FF68B2 /* Release */, 250 | ); 251 | defaultConfigurationIsVisible = 0; 252 | defaultConfigurationName = Release; 253 | }; 254 | /* End XCConfigurationList section */ 255 | }; 256 | rootObject = 9D149E3D1B82226B00FF68B2 /* Project object */; 257 | } 258 | -------------------------------------------------------------------------------- /ffttest.xcodeproj/project.xcworkspace/contents.xcworkspacedata: -------------------------------------------------------------------------------- 1 | 2 | 4 | 6 | 7 | 8 | -------------------------------------------------------------------------------- /ffttest.xcodeproj/project.xcworkspace/xcuserdata/christopher.xcuserdatad/UserInterfaceState.xcuserstate: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/christopherhelf/Swift-FFT-Example/81b5eee9408a999e049be57c261de319252cf63e/ffttest.xcodeproj/project.xcworkspace/xcuserdata/christopher.xcuserdatad/UserInterfaceState.xcuserstate -------------------------------------------------------------------------------- /ffttest.xcodeproj/xcuserdata/christopher.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist: -------------------------------------------------------------------------------- 1 | 2 | 5 | 6 | -------------------------------------------------------------------------------- /ffttest.xcodeproj/xcuserdata/christopher.xcuserdatad/xcschemes/ffttest.xcscheme: -------------------------------------------------------------------------------- 1 | 2 | 5 | 8 | 9 | 15 | 21 | 22 | 23 | 24 | 25 | 30 | 31 | 32 | 33 | 39 | 40 | 41 | 42 | 51 | 53 | 59 | 60 | 61 | 62 | 63 | 64 | 70 | 72 | 78 | 79 | 80 | 81 | 83 | 84 | 87 | 88 | 89 | -------------------------------------------------------------------------------- /ffttest.xcodeproj/xcuserdata/christopher.xcuserdatad/xcschemes/xcschememanagement.plist: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | SchemeUserState 6 | 7 | ffttest.xcscheme 8 | 9 | orderHint 10 | 0 11 | 12 | 13 | SuppressBuildableAutocreation 14 | 15 | 9D149E441B82226B00FF68B2 16 | 17 | primary 18 | 19 | 20 | 21 | 22 | 23 | -------------------------------------------------------------------------------- /ffttest/fft.swift: -------------------------------------------------------------------------------- 1 | // 2 | // fft.swift 3 | // ffttest 4 | // 5 | // Created by Christopher Helf on 17.08.15. 6 | // Copyright (c) 2015-Present Christopher Helf. All rights reserved. 7 | // Adapted From https://gerrybeauregard.wordpress.com/2013/01/28/using-apples-vdspaccelerate-fft/ 8 | 9 | import Foundation 10 | import Accelerate 11 | 12 | class FFT { 13 | 14 | fileprivate func getFrequencies(_ N: Int, fps: Double) -> [Double] { 15 | // Create an Array with the Frequencies 16 | let freqs = (0.. ([Double], Int, Int) { 24 | var minIdx = freqs.count+1 25 | var maxIdx = -1 26 | 27 | let bandPassFilter: [Double] = freqs.map { 28 | if ($0 >= self.lowerFreq && $0 <= self.higherFreq) { 29 | return 1.0 30 | } else { 31 | return 0.0 32 | } 33 | } 34 | 35 | for (i, element) in bandPassFilter.enumerated() { 36 | if (element == 1.0) { 37 | if(imaxIdx || maxIdx == -1) { 41 | maxIdx=i 42 | } 43 | } 44 | } 45 | 46 | assert(maxIdx != -1) 47 | assert(minIdx != freqs.count+1) 48 | 49 | return (bandPassFilter, minIdx, maxIdx) 50 | } 51 | 52 | func calculate(_ _values: [Double], fps: Double) { 53 | // ---------------------------------------------------------------- 54 | // Copy of our input 55 | // ---------------------------------------------------------------- 56 | let values1 = _values 57 | var values = values1 // need this to avoid error below 58 | 59 | // ---------------------------------------------------------------- 60 | // Size Variables 61 | // ---------------------------------------------------------------- 62 | let N = values.count 63 | let N2 = vDSP_Length(N/2) 64 | let LOG_N = vDSP_Length(log2(Float(values.count))) 65 | 66 | // ---------------------------------------------------------------- 67 | // FFT & Variables Setup 68 | // ---------------------------------------------------------------- 69 | let fftSetup: FFTSetupD = vDSP_create_fftsetupD(LOG_N, FFTRadix(kFFTRadix2))! 70 | 71 | // We need complex buffers in two different formats! 72 | var tempComplex : [DSPDoubleComplex] = [DSPDoubleComplex](repeating: DSPDoubleComplex(), count: N/2) 73 | 74 | var tempSplitComplexReal : [Double] = [Double](repeating: 0.0, count: N/2) 75 | var tempSplitComplexImag : [Double] = [Double](repeating: 0.0, count: N/2) 76 | var tempSplitComplex : DSPDoubleSplitComplex = DSPDoubleSplitComplex(realp: &tempSplitComplexReal, imagp: &tempSplitComplexImag) 77 | 78 | // For polar coordinates 79 | var mag : [Double] = [Double](repeating: 0.0, count: N/2) 80 | var phase : [Double] = [Double](repeating: 0.0, count: N/2) 81 | 82 | // ---------------------------------------------------------------- 83 | // Forward FFT 84 | // ---------------------------------------------------------------- 85 | 86 | var valuesAsComplex : UnsafeMutablePointer? = nil 87 | 88 | values.withUnsafeMutableBytes { 89 | valuesAsComplex = $0.baseAddress?.bindMemory(to: DSPDoubleComplex.self, capacity: values1.count) 90 | } 91 | 92 | // Scramble-pack the real data into complex buffer in just the way that's 93 | // required by the real-to-complex FFT function that follows. 94 | vDSP_ctozD(valuesAsComplex!, 2, &tempSplitComplex, 1, N2); 95 | 96 | // Do real->complex forward FFT 97 | vDSP_fft_zripD(fftSetup, &tempSplitComplex, 1, LOG_N, FFTDirection(FFT_FORWARD)); 98 | 99 | // ---------------------------------------------------------------- 100 | // Get the Frequency Spectrum 101 | // ---------------------------------------------------------------- 102 | 103 | var fftMagnitudes = [Double](repeating: 0.0, count: N/2) 104 | vDSP_zvmagsD(&tempSplitComplex, 1, &fftMagnitudes, 1, N2); 105 | 106 | // vDSP_zvmagsD returns squares of the FFT magnitudes, so take the root here 107 | let roots = sqrt(fftMagnitudes) 108 | 109 | // Normalize the Amplitudes 110 | var fullSpectrum = [Double](repeating: 0.0, count: N/2) 111 | vDSP_vsmulD(roots, vDSP_Stride(1), [1.0 / Double(N)], &fullSpectrum, 1, N2) 112 | 113 | // ---------------------------------------------------------------- 114 | // Convert from complex/rectangular (real, imaginary) coordinates 115 | // to polar (magnitude and phase) coordinates. 116 | // ---------------------------------------------------------------- 117 | 118 | vDSP_zvabsD(&tempSplitComplex, 1, &mag, 1, N2); 119 | 120 | // Beware: Outputted phase here between -PI and +PI 121 | // https://developer.apple.com/library/prerelease/ios/documentation/Accelerate/Reference/vDSPRef/index.html#//apple_ref/c/func/vDSP_zvphasD 122 | vDSP_zvphasD(&tempSplitComplex, 1, &phase, 1, N2); 123 | 124 | // ---------------------------------------------------------------- 125 | // Bandpass Filtering 126 | // ---------------------------------------------------------------- 127 | 128 | // Get the Frequencies for the current Framerate 129 | let freqs = getFrequencies(N,fps: fps) 130 | // Get a Bandpass Filter 131 | let bandPassFilter = generateBandPassFilter(freqs) 132 | 133 | // Multiply phase and magnitude with the bandpass filter 134 | mag = mul(mag, y: bandPassFilter.0) 135 | phase = mul(phase, y: bandPassFilter.0) 136 | 137 | // Output Variables 138 | let filteredSpectrum = mul(fullSpectrum, y: bandPassFilter.0) 139 | var filteredPhase = phase 140 | 141 | // ---------------------------------------------------------------- 142 | // Determine Maximum Frequency 143 | // ---------------------------------------------------------------- 144 | let maxFrequencyResult = max(filteredSpectrum) 145 | let maxFrequency = freqs[maxFrequencyResult.1] 146 | let maxPhase = filteredPhase[maxFrequencyResult.1] 147 | 148 | print("Amplitude: \(maxFrequencyResult.0)") 149 | print("Frequency: \(maxFrequency)") 150 | print("Phase: \(maxPhase + .pi / 2)") 151 | 152 | // ---------------------------------------------------------------- 153 | // Convert from polar coordinates back to rectangular coordinates. 154 | // ---------------------------------------------------------------- 155 | 156 | tempSplitComplex = DSPDoubleSplitComplex(realp: &mag, imagp: &phase) 157 | 158 | var complexAsValue : UnsafeMutablePointer? = nil 159 | 160 | tempComplex.withUnsafeMutableBytes { 161 | complexAsValue = $0.baseAddress?.bindMemory(to: Double.self, capacity: values.count) 162 | } 163 | 164 | vDSP_ztocD(&tempSplitComplex, 1, &tempComplex, 2, N2); 165 | vDSP_rectD(complexAsValue!, 2, complexAsValue!, 2, N2); 166 | vDSP_ctozD(&tempComplex, 2, &tempSplitComplex, 1, N2); 167 | 168 | // ---------------------------------------------------------------- 169 | // Do Inverse FFT 170 | // ---------------------------------------------------------------- 171 | 172 | // Create result 173 | var result : [Double] = [Double](repeating: 0.0, count: N) 174 | var resultAsComplex : UnsafeMutablePointer? = nil 175 | 176 | result.withUnsafeMutableBytes { 177 | resultAsComplex = $0.baseAddress?.bindMemory(to: DSPDoubleComplex.self, capacity: values.count) 178 | } 179 | 180 | // Do complex->real inverse FFT. 181 | vDSP_fft_zripD(fftSetup, &tempSplitComplex, 1, LOG_N, FFTDirection(FFT_INVERSE)); 182 | 183 | // This leaves result in packed format. Here we unpack it into a real vector. 184 | vDSP_ztocD(&tempSplitComplex, 1, resultAsComplex!, 2, N2); 185 | 186 | // Neither the forward nor inverse FFT does any scaling. Here we compensate for that. 187 | var scale : Double = 0.5/Double(N); 188 | var copyOfResult = result; 189 | vDSP_vsmulD(&result, 1, &scale, ©OfResult, 1, vDSP_Length(N)); 190 | result = copyOfResult 191 | 192 | // Print Result 193 | for k in 0 ..< N { 194 | print("\(k) \(values[k]) \(result[k])") 195 | } 196 | } 197 | 198 | // The bandpass frequencies 199 | let lowerFreq : Double = 3 200 | let higherFreq: Double = 5 201 | 202 | // Some Math functions on Arrays 203 | func mul(_ x: [Double], y: [Double]) -> [Double] { 204 | var results = [Double](repeating: 0.0, count: x.count) 205 | vDSP_vmulD(x, 1, y, 1, &results, 1, vDSP_Length(x.count)) 206 | 207 | return results 208 | } 209 | 210 | func sqrt(_ x: [Double]) -> [Double] { 211 | var results = [Double](repeating: 0.0, count: x.count) 212 | vvsqrt(&results, x, [Int32(x.count)]) 213 | 214 | return results 215 | } 216 | 217 | func max(_ x: [Double]) -> (Double, Int) { 218 | var result: Double = 0.0 219 | var idx : vDSP_Length = vDSP_Length(0) 220 | vDSP_maxviD(x, 1, &result, &idx, vDSP_Length(x.count)) 221 | 222 | return (result, Int(idx)) 223 | } 224 | } 225 | -------------------------------------------------------------------------------- /ffttest/main.swift: -------------------------------------------------------------------------------- 1 | // 2 | // main.swift 3 | // ffttest 4 | // 5 | // Created by Christopher Helf on 17.08.15. 6 | // Copyright (c) 2015-Present Christopher Helf. All rights reserved. 7 | // 8 | 9 | import Foundation 10 | import Accelerate 11 | 12 | var fft = FFT() 13 | 14 | let n = 512 // Should be power of two for the FFT 15 | let frequency1 = 4.0 16 | let phase1 = 0.0 17 | let amplitude1 = 8.0 18 | let seconds = 2.0 19 | let fps = Double(n)/seconds 20 | 21 | var sineWave = (0..