349. Digital Signal Processing

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349. Digital Signal Processing

 

 

CATEGORY:Music, Mastering,Mixing & Writing – 400 Courses

COURSE NUMBER: 349

FEES: 555/- INR only

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BOOKS/ MANUALS: Pages

Syllabus

Preface v
Acknowledgements ix
About the Book Cover Design xi
1. Acoustics, Hearing Limitations, and Sampling 1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 The Sine Tone . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Human Hearing and Its Limitations . . . . . . . . . . . . 4
3.1 Duration . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Pitch . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3 Amplitude and sound levels . . . . . . . . . . . . 6
3.3.1 Sound intensity level (SIL) . . . . . . . 6
3.3.2 Sound pressure level (SPL) . . . . . . . 8
3.3.3 Just noticeable difference (JND) . . . . 8
3.3.4 Equal loudness curve . . . . . . . . . . . 8
3.4 Auditory masking . . . . . . . . . . . . . . . . . . 11
4 Sampling: The Art of Being Discrete . . . . . . . . . . . 13
4.1 Sampling theorem . . . . . . . . . . . . . . . . . . 18
4.2 Aliasing . . . . . . . . . . . . . . . . . . . . . . . 20
5 Quantization and Pulse Code Modulation (PCM) . . . . 26
5.1 SNR and QSNR . . . . . . . . . . . . . . . . . . . 28
6 DC Component . . . . . . . . . . . . . . . . . . . . . . . 29
7 Distortion and Square Waves . . . . . . . . . . . . . . . . 31
7.1 Dithering . . . . . . . . . . . . . . . . . . . . . . . 33
8 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 37
References and Further Reading . . . . . . . . . . . . . . . . . 38
2. Time-Domain Signal Processing I 40
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 40
2 Amplitude Envelope and ADSR . . . . . . . . . . . . . . 41
3 Wavetable Synthesis . . . . . . . . . . . . . . . . . . . . 43
4 Windowing, RMS, and Amplitude Envelope . . . . . . . 46
4.1 Windowing: More details . . . . . . . . . . . . . . 46
4.2 RMS and amplitude envelope . . . . . . . . . . . 50
5 Time-Domain Fundamental Frequency Computation . . 53
5.1 Zero-crossing rate . . . . . . . . . . . . . . . . . . 54
5.2 Autocorrelation . . . . . . . . . . . . . . . . . . . 58
5.3 Cross-correlation . . . . . . . . . . . . . . . . . . 64
6 Sample Rate Conversion . . . . . . . . . . . . . . . . . . 65
6.1 Up-sampling . . . . . . . . . . . . . . . . . . . . . 65
6.2 Down-sampling . . . . . . . . . . . . . . . . . . . 66
7 Overlap and Add (OLA) . . . . . . . . . . . . . . . . . . 68
7.1 OLA: Problems and solutions . . . . . . . . . . . 71
8 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 72
References and Further Reading . . . . . . . . . . . . . . . . . 74
3. Time-Domain Processes II 75
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 75
2 Granular Synthesis . . . . . . . . . . . . . . . . . . . . . 75
2.1 Basic granular synthesis parameters . . . . . . . . 76
2.2 Asynchronous granular synthesis . . . . . . . . . 79
2.3 Pitch shifting and time stretching/compression . 80
2.4 Sound morphing with granular synthesis . . . . . 81
3 Amplitude Distortion and Waveshaping . . . . . . . . . . 81
3.1 Dynamic compressor . . . . . . . . . . . . . . . . 83
3.2 Distortion . . . . . . . . . . . . . . . . . . . . . . 85
3.3 Dynamic expander . . . . . . . . . . . . . . . . . 86
3.4 Tape saturation . . . . . . . . . . . . . . . . . . . 87
3.5 Waveshaping synthesis . . . . . . . . . . . . . . . 87
3.5.1 Chebychev polynomials
of the 1st kind . . . . . . . . . . . . . . 88
4 Some Familiar Time-Domain DSP Effects . . . . . . . . 91
4.1 Equal power panning . . . . . . . . . . . . . . . . 91
4.2 Delays . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.1 Echo, chorus, and flanging . . . . . . . . 92
5 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 95
References and Further Reading . . . . . . . . . . . . . . . . . 96
4. Sine Waves 97
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 97
2 Sinusoids Revisited . . . . . . . . . . . . . . . . . . . . . 98
3 Imaginary, Complex Numbers, and Euler’s Formula . . . 99
3.1 Euler’s formula . . . . . . . . . . . . . . . . . . . 101
4 Sinusoidal Modulation Techniques I: Amplitude . . . . . 102
4.1 Beating . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2 Amplitude modulation and ring modulation . . . 105
4.3 Amplitude modulation (AM) . . . . . . . . . . . 106
4.4 Ring modulation . . . . . . . . . . . . . . . . . . 108
4.4.1 Ring modulation with complex
signals . . . . . . . . . . . . . . . . . . . 108
5 Sinusoidal Modulation Techniques II: Frequency . . . . . 110
5.1 FM: Sidebands and the Bessel function . . . . . . 111
5.2 Modulation index . . . . . . . . . . . . . . . . . . 115
5.3 General topics in FM control parameters . . . . . 116
6 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 118
References and Further Reading . . . . . . . . . . . . . . . . . 121
5. Linear Time-Invariant Systems 122
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 122
2 Difference Equations: Starting with the Moving
Average Algorithm . . . . . . . . . . . . . . . . . . . . . 123
2.1 Causality . . . . . . . . . . . . . . . . . . . . . . . 125
2.2 Difference equations: General form . . . . . . . . 125
3 Linear-Time Invariant (LTI) Systems . . . . . . . . . . . 127
3.1 Linearity property: Scalability
and superposition . . . . . . . . . . . . . . . . . . 128
3.2 Time-invariance property:
Time-shift invariance . . . . . . . . . . . . . . . . 129
3.3 Importance of LTI systems in DSP . . . . . . . . 131
4 Impulse Response . . . . . . . . . . . . . . . . . . . . . . 132
4.1 Finite impulse response (FIR) and infinite
impulse response (IIR) . . . . . . . . . . . . . . . 135
4.2 Stability and IIR systems . . . . . . . . . . . . . 136
5 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.1 Convolution “Need to Knows” . . . . . . . . . . . 140
6 System Diagrams and Digital Building Blocks . . . . . . 141
7 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 143
6. Frequency Response 145
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 145
2 The Frequency Response . . . . . . . . . . . . . . . . . . 146
2.1 Characteristics and properties of H(ejθ) . . . . . 149
2.1.1 Frequency range and Nyquist revisited . 149
2.1.2 H(ejθ) and periodicity property . . . . . 154
2.1.3 Symmetry . . . . . . . . . . . . . . . . . 155
2.2 More stuff on the frequency response . . . . . . . 156
3 Phase Response and Phase Distortion . . . . . . . . . . . 160
3.1 Phase delay . . . . . . . . . . . . . . . . . . . . . 163
3.2 Linearity and phase . . . . . . . . . . . . . . . . . 165
3.3 Phase response and continuous phase . . . . . . . 167
3.4 Group delay . . . . . . . . . . . . . . . . . . . . . 168
4 The (Almost) Magical Z-Transform . . . . . . . . . . . . 172
4.1 What does all this mean? Part I . . . . . . . . . . 174
4.2 What does all this mean? Part II: poles
and zeros . . . . . . . . . . . . . . . . . . . . . . . 175
4.3 What does all this mean? Part III:
the unit circle and the z-plane . . . . . . . . . . . 176
4.4 More “complex” systems . . . . . . . . . . . . . . 181
5 Region of Convergence (ROC) . . . . . . . . . . . . . . . 181
5.1 Causal system ROC . . . . . . . . . . . . . . . . . 186
5.2 Mixed-causality systems . . . . . . . . . . . . . . 187
5.3 ROC summary . . . . . . . . . . . . . . . . . . . 188
6 Stability and the Unit Circle . . . . . . . . . . . . . . . . 188
7 The Inverse Z-Transform . . . . . . . . . . . . . . . . . . 190
7.1 Long division method . . . . . . . . . . . . . . . . 191
7.2 Taylor series expansion method . . . . . . . . . . 193
7.3 Contour integration/residue theorem method . . 195
8 Useful Tools in MATLABR . . . . . . . . . . . . . . . . 197
9 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 198
References and Further Reading . . . . . . . . . . . . . . . . . 199
7. Filters 200
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 200
2 Low/High/Band-Pass and Band-Stop Filters . . . . . . . 201
2.1 Filter design specifications . . . . . . . . . . . . . 203
2.2 Passband, stopband, and transition band . . . . . 204
2.3 Cutoff frequency . . . . . . . . . . . . . . . . . . 205
2.4 Filter order, filter sharpness, and ripple . . . . . . 205
2.5 MATLABR filter design tools . . . . . . . . . . . 219
3 Filter Examples . . . . . . . . . . . . . . . . . . . . . . . 222
3.1 Subtractive synthesis and filters . . . . . . . . . . 223
3.2 Bi-quadratic filter (a.k.a. Bi-quad filter)
and the Wah-Wah filter . . . . . . . . . . . . . . 225
3.3 The Comb-filter . . . . . . . . . . . . . . . . . . . 233
3.3.1 Comb-filter interpretation . . . . . . . . 235
3.3.2 Comb-filter examples . . . . . . . . . . . 238
3.4 String vibration and standing waves . . . . . . . . 242
3.5 Physical modeling synthesis and the plucked
string model . . . . . . . . . . . . . . . . . . . . . 245
3.5.1 Direct implementation of difference
equations . . . . . . . . . . . . . . . . . 253
3.6 Phase as a filtering application . . . . . . . . . . 254
3.6.1 The chorus effect . . . . . . . . . . . . . 254
3.6.2 Multi-tap filters and filter banks . . . . 256
3.6.3 Fractional delay . . . . . . . . . . . . . . 259
3.6.4 The flanger effect . . . . . . . . . . . . . 261
3.6.5 The all-pass filter . . . . . . . . . . . . . 262
3.6.6 Very basic all-pass filter reverb . . . . . 266
4 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 272
References and Further Reading . . . . . . . . . . . . . . . . . 274
8. Frequency-Domain and the Fourier Transform 276
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 276
2 Additive Synthesis . . . . . . . . . . . . . . . . . . . . . 277
3 The Fourier Transform . . . . . . . . . . . . . . . . . . . 280
4 The Discrete-Time Fourier Transform (DTFT)
and the Discrete Fourier Transform (DFT) . . . . . . . . 281
4.1 Magnitude, Phase, and Other Basic Properties
of the DFT . . . . . . . . . . . . . . . . . . . . . 288
4.2 Time Resolution vs. Frequency Resolution
in DFTs . . . . . . . . . . . . . . . . . . . . . . . 289
5 Short-Time Fourier Transform (STFT) . . . . . . . . . . 292
6 Zero Padding . . . . . . . . . . . . . . . . . . . . . . . . 293
7 Aliasing Revisited . . . . . . . . . . . . . . . . . . . . . . 295
8 Another Look: Down-Sampling and Up-Sampling
Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
8.1 Down-Sampling . . . . . . . . . . . . . . . . . . . 298
8.2 Up-Sampling . . . . . . . . . . . . . . . . . . . . . 302
9 Windowing Revisited: A View from the
Frequency-Domain Side . . . . . . . . . . . . . . . . . . . 304
9.1 Rectangular Window . . . . . . . . . . . . . . . . 310
9.2 Hann Window . . . . . . . . . . . . . . . . . . . . 310
9.3 Hamming Window . . . . . . . . . . . . . . . . . 311
9.4 Blackman Window . . . . . . . . . . . . . . . . . 312
9.5 Chebychev and Kaiser Windows . . . . . . . . . . 312
9.6 Not Just More Windowing Stuff . . . . . . . . . . 313
10 The Fast Fourier Transform (FFT) . . . . . . . . . . . . 319
11 Convolution (also) Revisited . . . . . . . . . . . . . . . . 321
11.1 Circular Convolution and Time-Aliasing . . . . . 322
12 One More Look at Dithering . . . . . . . . . . . . . . . . 325
13 Spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . 327
14 Fourier Transform Properties and Summary . . . . . . . 329
15 MATLABR and Fourier Transform . . . . . . . . . . . . 331
16 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 331
References and Further Reading . . . . . . . . . . . . . . . . . 332
9. Spectral Analysis, Vocoders, and
other Goodies 333
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 333
1.1 Musical signals and important nomenclatures . . 333
2 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . 335
2.1 Long-term average spectrum (LTAS) . . . . . . . 336
2.2 Log vs. linear . . . . . . . . . . . . . . . . . . . . 336
2.3 Spectral peaks, valleys, and spectral envelope . . 340
2.4 Extraction of fundamental frequency
and harmonics . . . . . . . . . . . . . . . . . . . . 344
2.4.1 Inverse comb-filtering . . . . . . . . . . 345
2.4.2 Cepstrum analysis . . . . . . . . . . . . 349
2.4.3 Harmonic product spectrum . . . . . . . 350
3 Vocoders (Voice Coders) . . . . . . . . . . . . . . . . . . 352
3.1 Channel-vocoder . . . . . . . . . . . . . . . . . . 352
3.1.1 Filter banks, envelope followers,
and the encoder . . . . . . . . . . . . . . 354
3.1.2 Voiced and unvoiced analysis
and the decoder . . . . . . . . . . . . . . 356
3.1.3 Voiced and unvoiced decision-making . . 359
3.1.3.1 Zero-crossing analysis . . . . 359
3.1.3.2 Pre-emphasized energy ratio 363
3.1.3.3 Low-band to full-band
energy ratio . . . . . . . . . 363
3.1.3.4 Spectral flatness measure . . 364
3.2 Linear predictive coding (LPC) . . . . . . . . . . 366
3.3 LPC coefficient computation . . . . . . . . . . . . 371
3.4 The phase vocoder . . . . . . . . . . . . . . . . . 373
3.4.1 Estimation of instantaneous
frequency . . . . . . . . . . . . . . . . . 375
3.4.2 Phase unwrapping . . . . . . . . . . . . 377
3.4.3 Phase vocoder: Filter-bank
interpretation . . . . . . . . . . . . . . . 379
3.4.4 Phase vocoder: Fourier transform
interpretation . . . . . . . . . . . . . . . 385
3.4.5 Phase vocoder basics: Time
and pitch-shifting . . . . . . . . . . . . . 390
3.4.5.1 Time-shifting . . . . . . . . . 391
3.4.5.2 Pitch-shifting . . . . . . . . . 396
4 Research Topics in Computer Music . . . . . . . . . . . . 397
4.1 Salient feature extraction . . . . . . . . . . . . . . 397
4.1.1 Spectral envelope . . . . . . . . . . . . . 398
4.1.2 Spectral centroid . . . . . . . . . . . . . 399
4.1.3 Shimmer and Jitter . . . . . . . . . . . . 400
4.1.4 Spectral flux . . . . . . . . . . . . . . . 400
4.1.5 Log spectral spread . . . . . . . . . . . . 401
4.1.6 Roll-off . . . . . . . . . . . . . . . . . . 401
4.1.7 Attack time (rise time) . . . . . . . . . . 402
4.1.8 Amplitude modulation (Tremolo) . . . . 402
4.1.9 Temporal centroid . . . . . . . . . . . . 403
4.2 MIR (Music information retrieval) . . . . . . . . 403
4.2.1 Query-by-humming (QbH) . . . . . . . . 404
4.2.2 Automatic beat detection and rhythm
analysis . . . . . . . . . . . . . . . . . . 405
4.2.3 Automatic timbre recognition . . . . . . 406
4.3 FMS (feature modulation synthesis) . . . . . . . . 407
5 Musical Examples . . . . . . . . . . . . . . . . . . . . . . 409
References and Further Reading . . . . . . . . . . . . . . . . . 411
Appendix 415
1 To Scale or Not to Scale: That is the Question . . . . . . 415
1.1 Equal temperament scale . . . . . . . . . . . . . . 415
1.2 Just intonation . . . . . . . . . . . . . . . . . . . 416
1.3 Bark scale . . . . . . . . . . . . . . . . . . . . . . 416
1.4 Mel scale . . . . . . . . . . . . . . . . . . . . . . . 417
2 MATLAB Programs Used in This Book . . . . . . . . . 418
Index 423

……………………………………………………………………………………………………………………………………………………………………………………………………………………

 

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CATEGORY:Music, Mastering,Mixing & Writing – 400 Courses

COURSE NUMBER: 30

FEES: 555/- INR only

CERTIFICATE VALIDITY: Lifetime

CERTIFICATES DELIVERY: In 48 hours

……………………………………………………………………………………………………………………………………………………………………………………………………………………

 

Medifit  Courses Demo Certificate 

48 hours delivery

| International acceptance | Medical based | Job oriented | Lifetime validity | Most economical |

 

555 INR Demo Certificate – 2 months duration

Demo Certificate – 6 months duration

48 hours delivery after fees payment

48 hours delivery after fees payment

 

Medifit 48 hours Delivery

  Get your Certificates delivered by online mode in 48 hours after Fees payment. We try to deliver certificates in 24 hours, but the committed delivery hours are 48. Its,

Pay Today &
get Tomorrow

procedure, only by Medifit.

LIFETIME VALIDITY

Medifit issues Lifetime validity certificates for all Online Courses provided. No need to renew the certificates every 2 or 3 years. All Courses Certificates of Medifit are having Lifetime Validity. No need to renew these certificates every 2 or 3 years.

 

What makes the certificates of Medifit to get it recognized Internationally?

Vast number of students applying for Job in international market of Fitness through Medifits Online Courses Certificates. And most importantly, the Medical standards maintained, helps to acquire jobs internationally. This gives very strong International acceptance to Certificates of Medifit Courses.

 

ABOUT MEDIFIT ACADEMY CERTIFICATION COURSE:

Medifit Education Online Academy is an innovative, digital and engaging education platform that delivers fast track accredited courses and skills development courses instantly online, with no time limits, enabling individuals to study anywhere and anytime. We are proud to offer international standard courses that have helped our students build their careers across the globe.

HOW DO MEDIFIT ONLINE CERTIFICATE COURSES HELP?

Short term Professional Courses International Standards courses Opens Global opportunities Career defining Courses Skill Development Programmes Knowledge in short span Learn at your own pace Certification of Completion Immediate Earning Opportunities Positive Social Impact Optimistic Psychological Benefits Improved Standard of Living Study from anywhere & anytime Very Economical Fees