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ProblemCourse & topicStatus
DSP:010117Mathematical problem title
Dsp Aperiodic Autocorrelation LagsDsp Dtft Parseval Energy Density
Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review
—Prerequisite review: discrete LTI, DTFT, and z-transform conventionsDigital Signal Processing · Mixed review
—Digital-filter structures and implementationDigital Signal Processing · Mixed review
—Digital-filter structures and implementationDigital Signal Processing · Mixed review
—Digital-filter structures and implementationDigital Signal Processing · Mixed review
—Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review
—Sampling, multirate, and polyphase processingDigital Signal Processing · Mixed review
—DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review
—DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review
—DFT, FFT, and spectral leakageDigital Signal Processing · Mixed review
—FIR and IIR filter designDigital Signal Processing · Mixed review
—FIR and IIR filter designDigital Signal Processing · Mixed review
—Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review
—View access optionsDsp Rounding Quantizer Zero Input OrbitDsp Limit Cycle Versus Pole Stability
Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review
—Spectral estimation and finite-precision effectsDigital Signal Processing · Mixed review
—Showing 15 of 15 matching problems.
Aperiodic r[k] of (1,2,-1) is 6,0,-1 with |X|^2=6-2cos 2w and Parseval energy 6
Hilbert of 1+(-1)^n+2cos(πn/3)+3sin(πn/2) is 2sin(πn/3)-3cos(πn/2)
The symmetric FIR (1,2,3,4,3,2,1) is e^{-j3w}(4+6cos w+4cos 2w+2cos 3w) and folds to y=11
The moving sum 1+z^{-1}+z^{-2}+z^{-3} equals (1-z^{-4})/(1-z^{-1}) with removable value 4
The allpass (a+z^{-1})/(1+a z^{-1}) at a=1/2 has energy 1, τ(0)=1/3, and τ(π)=3
Upsampling cos(pi n/3) by 3 images at ±pi/9, ±5pi/9, ±7pi/9; gain-3 LPF recovers cos(pi m/9)
Type-I polyphase of (1,2,3,4,5,6) at M=3 gives y[2]=56 with 6 multiplies, not 18
Eight-point radix-2 DIT of (1,2,3,4,0,0,0,0) has X0=10, Parseval 240, and 12 butterflies
Goertzel at k=2 on the length-8 ramp pad gives G=2+2j and X2=e^{j omega}G=-2+2j
Periodic Hann N=8 hop 4 is COLA-1; a second Hann is not square-COLA and needs normalization
Prewarped 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)
The 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
AR(1) Yule–Walker with R[0]=4, R[1]=2 gives a=1/2, innovation 3, S(0)=12 and one-step MSE 3
Rounding y[n]=Q(0.75 y[n-1]) from y[-1]=1 locks at 0.5; truncation dies; the pole 0.75 is stable
An 8-point radix-2 FFT of x=4 overflows unscaled; /2 at each of 3 stages stores (4,0,...) with exponent 3