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Dsp Aperiodic Autocorrelation LagsDsp Dtft Parseval Energy Density

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Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review

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Dsp Discrete Hilbert TransformerDsp Analytic Signal Onesided Spectrum

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Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review

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Dsp Type I Linear Phase FactorDsp Folded Fir Arithmetic

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp Comb Moving Average IdentityDsp Canceled Pole Internal Overflow

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp First Order Allpass Pole ZeroDsp Allpass Group Delay Energy

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp Integer Expander Dtft ImagesDsp Ideal Interpolator Gain L

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Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review

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Dsp Type1 Polyphase DecompositionDsp Noble Identity Decimator Arithmetic

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Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review

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Dsp Radix2 Dit Bit Reversal ButterfliesDsp Eight Point Dft Parseval

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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Dsp Goertzel Recurrence SpecializedDsp Goertzel Phase TO Dft Bin

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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Dsp Periodic Hann Cola IdentityDsp Wola Square Cola Normalization

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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DSP:010527Prewarped bilinear of Omega_c/(s+Omega_c) at wc=pi/3 is the stable Hd with H(1)=1 and |H(wc)|=1/sqrt(2)

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Dsp Bilinear Prewarp Analog CutoffDsp First Order Bilinear Gain Pole

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FIR and IIR filter designDigital Signal Processing · Mixed review

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DSP:010528The Type-I taps (1/8,1/4,1/4,1/4,1/8) notch pi/2 and pi, have delay 2, and are linear phase not zero phase

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Dsp Type I Three Point InterpolationDsp Linear Phase Amplitude Zeros

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FIR and IIR filter designDigital Signal Processing · Mixed review

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DSP:010629AR(1) Yule–Walker with R[0]=4, R[1]=2 gives a=1/2, innovation 3, S(0)=12 and one-step MSE 3

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Dsp Ar1 Yule Walker LagsDsp Ar1 Parametric Psd Predictor

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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DSP:010630Rounding y[n]=Q(0.75 y[n-1]) from y[-1]=1 locks at 0.5; truncation dies; the pole 0.75 is stable

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Dsp Rounding Quantizer Zero Input OrbitDsp Limit Cycle Versus Pole Stability

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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DSP:010631An 8-point radix-2 FFT of x=4 overflows unscaled; /2 at each of 3 stages stores (4,0,...) with exponent 3

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Dsp Constant Sequence Radix2 DftDsp Block Floating Fft Exponent

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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Problem library

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Problem results

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Dsp Aperiodic Autocorrelation LagsDsp Dtft Parseval Energy Density

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Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review

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Dsp Discrete Hilbert TransformerDsp Analytic Signal Onesided Spectrum

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Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review

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Dsp Type I Linear Phase FactorDsp Folded Fir Arithmetic

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp Comb Moving Average IdentityDsp Canceled Pole Internal Overflow

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp First Order Allpass Pole ZeroDsp Allpass Group Delay Energy

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Digital-filter structures and implementationDigital Signal Processing · Mixed review

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Dsp Integer Expander Dtft ImagesDsp Ideal Interpolator Gain L

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Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review

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Dsp Type1 Polyphase DecompositionDsp Noble Identity Decimator Arithmetic

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Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review

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Dsp Radix2 Dit Bit Reversal ButterfliesDsp Eight Point Dft Parseval

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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Dsp Goertzel Recurrence SpecializedDsp Goertzel Phase TO Dft Bin

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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Dsp Periodic Hann Cola IdentityDsp Wola Square Cola Normalization

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DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review

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DSP:010527Prewarped bilinear of Omega_c/(s+Omega_c) at wc=pi/3 is the stable Hd with H(1)=1 and |H(wc)|=1/sqrt(2)

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Dsp Bilinear Prewarp Analog CutoffDsp First Order Bilinear Gain Pole

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FIR and IIR filter designDigital Signal Processing · Mixed review

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DSP:010528The Type-I taps (1/8,1/4,1/4,1/4,1/8) notch pi/2 and pi, have delay 2, and are linear phase not zero phase

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Dsp Type I Three Point InterpolationDsp Linear Phase Amplitude Zeros

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FIR and IIR filter designDigital Signal Processing · Mixed review

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DSP:010629AR(1) Yule–Walker with R[0]=4, R[1]=2 gives a=1/2, innovation 3, S(0)=12 and one-step MSE 3

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Dsp Ar1 Yule Walker LagsDsp Ar1 Parametric Psd Predictor

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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DSP:010630Rounding y[n]=Q(0.75 y[n-1]) from y[-1]=1 locks at 0.5; truncation dies; the pole 0.75 is stable

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Dsp Rounding Quantizer Zero Input OrbitDsp Limit Cycle Versus Pole Stability

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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DSP:010631An 8-point radix-2 FFT of x=4 overflows unscaled; /2 at each of 3 stages stores (4,0,...) with exponent 3

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Dsp Constant Sequence Radix2 DftDsp Block Floating Fft Exponent

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Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review

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Problem results

DSP:010527Prewarped bilinear of Omega_c/(s+Omega_c) at wc=pi/3 is the stable Hd with H(1)=1 and |H(wc)|=1/sqrt(2)

DSP:010528The Type-I taps (1/8,1/4,1/4,1/4,1/8) notch pi/2 and pi, have delay 2, and are linear phase not zero phase

DSP:010629AR(1) Yule–Walker with R[0]=4, R[1]=2 gives a=1/2, innovation 3, S(0)=12 and one-step MSE 3

DSP:010630Rounding y[n]=Q(0.75 y[n-1]) from y[-1]=1 locks at 0.5; truncation dies; the pole 0.75 is stable

DSP:010631An 8-point radix-2 FFT of x=4 overflows unscaled; /2 at each of 3 stages stores (4,0,...) with exponent 3

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Problem results

DSP:010527Prewarped bilinear of Omega_c/(s+Omega_c) at wc=pi/3 is the stable Hd with H(1)=1 and |H(wc)|=1/sqrt(2)

DSP:010528The Type-I taps (1/8,1/4,1/4,1/4,1/8) notch pi/2 and pi, have delay 2, and are linear phase not zero phase

DSP:010629AR(1) Yule–Walker with R[0]=4, R[1]=2 gives a=1/2, innovation 3, S(0)=12 and one-step MSE 3

DSP:010630Rounding y[n]=Q(0.75 y[n-1]) from y[-1]=1 locks at 0.5; truncation dies; the pole 0.75 is stable

DSP:010631An 8-point radix-2 FFT of x=4 overflows unscaled; /2 at each of 3 stages stores (4,0,...) with exponent 3

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Problem results

DSP:010117Aperiodic r[k] of (1,2,-1) is 6,0,-1 with |X|^2=6-2cos 2w and Parseval energy 6

DSP:010118Hilbert of 1+(-1)^n+2cos(πn/3)+3sin(πn/2) is 2sin(πn/3)-3cos(πn/2)

DSP:010219The symmetric FIR (1,2,3,4,3,2,1) is e^{-j3w}(4+6cos w+4cos 2w+2cos 3w) and folds to y=11

DSP:010220The moving sum 1+z^{-1}+z^{-2}+z^{-3} equals (1-z^{-4})/(1-z^{-1}) with removable value 4

DSP:010221The allpass (a+z^{-1})/(1+a z^{-1}) at a=1/2 has energy 1, τ(0)=1/3, and τ(π)=3

DSP:010322Upsampling cos(pi n/3) by 3 images at ±pi/9, ±5pi/9, ±7pi/9; gain-3 LPF recovers cos(pi m/9)

DSP:010323Type-I polyphase of (1,2,3,4,5,6) at M=3 gives y[2]=56 with 6 multiplies, not 18

DSP:010424Eight-point radix-2 DIT of (1,2,3,4,0,0,0,0) has X0=10, Parseval 240, and 12 butterflies

DSP:010425Goertzel at k=2 on the length-8 ramp pad gives G=2+2j and X2=e^{j omega}G=-2+2j

DSP:010426Periodic Hann N=8 hop 4 is COLA-1; a second Hann is not square-COLA and needs normalization

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Problem results

DSP:010117Aperiodic r[k] of (1,2,-1) is 6,0,-1 with |X|^2=6-2cos 2w and Parseval energy 6

DSP:010118Hilbert of 1+(-1)^n+2cos(πn/3)+3sin(πn/2) is 2sin(πn/3)-3cos(πn/2)

DSP:010219The symmetric FIR (1,2,3,4,3,2,1) is e^{-j3w}(4+6cos w+4cos 2w+2cos 3w) and folds to y=11

DSP:010220The moving sum 1+z^{-1}+z^{-2}+z^{-3} equals (1-z^{-4})/(1-z^{-1}) with removable value 4

DSP:010221The allpass (a+z^{-1})/(1+a z^{-1}) at a=1/2 has energy 1, τ(0)=1/3, and τ(π)=3

DSP:010322Upsampling cos(pi n/3) by 3 images at ±pi/9, ±5pi/9, ±7pi/9; gain-3 LPF recovers cos(pi m/9)

DSP:010323Type-I polyphase of (1,2,3,4,5,6) at M=3 gives y[2]=56 with 6 multiplies, not 18

DSP:010424Eight-point radix-2 DIT of (1,2,3,4,0,0,0,0) has X0=10, Parseval 240, and 12 butterflies

DSP:010425Goertzel at k=2 on the length-8 ramp pad gives G=2+2j and X2=e^{j omega}G=-2+2j

DSP:010426Periodic Hann N=8 hop 4 is COLA-1; a second Hann is not square-COLA and needs normalization