Digital Signal Processing

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• Deterministic vs. random, periodic vs. aperiodic signals ~12 min
• Energy signals and power signals ~12 min
• Even and odd signals, and the even/odd decomposition ~12 min
• Exponential and sinusoidal sequences ~12 min
• Sequence transformations: shifting and reflection ~12 min
• Sequence transformations: time-scaling and amplitude-scaling ~12 min
• System properties: memory, causality, and stability ~14 min
• Linearity and time-invariance -- why LTI systems are special ~14 min
• A DSP application survey ~10 min

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• The convolution sum, derived from the sifting property ~14 min
• Graphical and analytical convolution evaluation ~14 min
• LTI system properties via convolution algebra ~12 min
• Numerical convolution: stream vs. block processing ~14 min
• Linear constant-coefficient difference equations ~14 min
• Recursive vs. non-recursive systems, and what that means for memory ~12 min
• Homogeneous and particular solutions ~14 min
• Zero-input and zero-state response ~12 min
• Real-time FIR implementation, a first look ~12 min

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• The Fourier transform, its properties, and the convolution theorem, revisited ~12 min
• Discrete-time sinusoid periodicity, revisited for the frequency domain ~10 min
• The discrete-time Fourier transform (DTFT), defined ~14 min
• DTFT properties ~12 min
• Periodicity of the DTFT ~10 min
• The four Fourier representations, unified ~12 min
• Magnitude and phase spectra: reading a DTFT ~12 min
• Relating a system's frequency response to its difference equation ~12 min

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• Sinusoidal steady-state response ~12 min
• Frequency-domain response to general inputs ~10 min
• Magnitude and phase (group-delay) distortion ~12 min
• Ideal vs. practical filter types: tolerance diagrams ~12 min
• The z-transform: why a transform beyond the DTFT is needed ~10 min
• The z-transform: definition, region of convergence, and common pairs ~14 min
• The inverse z-transform ~14 min
• Z-transform properties ~12 min
• Poles, zeros, and the system function H(z) ~14 min

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• Pole-zero geometry and time-domain behavior ~12 min
• The vector argument for frequency-response shape ~12 min
• A first filter design by direct pole-zero placement ~12 min
• Magnitude-phase relationships ~12 min
• Allpass systems ~12 min
• Minimum-phase systems and minimum-phase/allpass decomposition ~14 min
• Invertibility of LTI systems ~12 min
• Why pole-zero intuition is load-bearing for filter design ~10 min

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• Recall: the Nyquist-Shannon theorem and aliasing ~10 min
• The "impersonation" framing of aliasing ~10 min
• Ideal reconstruction and bandlimited (sinc) interpolation ~12 min
• Practical, non-ideal sampling and reconstruction ~12 min
• The sandwich model of continuous-signal processing ~10 min
• Bandpass sampling ~12 min
• Deliberately violating the Nyquist criterion ~10 min
• A first look at quantization ~8 min
• Two-dimensional sampling ~8 min

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• Recall: the DFT definition and circular convolution ~12 min
• Why only the DFT is exactly computable ~10 min
• The DFT as a sampled DTFT ~10 min
• Linear convolution via the DFT and zero-padding ~14 min
• Spectral leakage ~12 min
• Window functions and their trade-offs ~14 min
• The spectrogram of a synthesized signal ~12 min
• Fourier-based signal analysis, worked end to end ~12 min

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• Direct DFT computation: an O(N²) baseline ~10 min
• The FFT idea via matrix factorization ~14 min
• Decimation-in-time FFT and the butterfly diagram ~14 min
• Decimation-in-frequency FFT ~12 min
• Bit-reversal and in-place computation ~12 min
• O(N log N) versus O(N²), measured ~10 min
• Other FFT families ~8 min

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• Block diagrams and signal-flow graphs ~10 min
• Direct form I and direct form II ~12 min
• Cascade and parallel structures ~12 min
• FIR structures and the linear-phase folded form ~12 min
• Lattice structures and reflection coefficients ~14 min
• The lattice-coefficient stability test ~12 min
• Why structure choice matters: coefficient sensitivity ~10 min

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• The filter-design problem: five stages ~10 min
• Linear-phase FIR filters and the four symmetry types ~12 min
• The windowing method ~12 min
• The frequency-sampling method ~12 min
• Chebyshev polynomials and minimax approximation ~12 min
• The Paley-Wiener theorem ~12 min
• The alternation theorem and equiripple design ~14 min
• Special FIR filters: differentiators ~10 min
• Special FIR filters: Hilbert transformers ~10 min

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• The Butterworth analog prototype ~12 min
• The Chebyshev I analog prototype ~12 min
• Chebyshev II and elliptic prototypes ~10 min
• The three conditions for a valid transformation ~10 min
• The impulse-invariance transformation ~12 min
• The bilinear transformation ~12 min
• Frequency prewarping ~10 min
• Frequency transformations: lowpass to highpass, bandpass, bandstop ~12 min
• Choosing FIR vs. IIR ~10 min

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• Recall: random variables, joint distributions, and covariance ~10 min
• Why deterministic-signal tools don't apply to random signals ~10 min
• Stationarity of random processes ~10 min
• Wide-sense stationarity and ergodicity ~12 min
• The autocorrelation sequence ~12 min
• Power spectral density ~12 min
• White noise and AR/MA/ARMA process models ~12 min
• Linking process statistics to filter design ~10 min

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• Estimating statistics from data: bias, consistency, asymptotic unbiasedness ~12 min
• The periodogram: a poor PSD estimator ~12 min
• Bartlett and Welch averaging ~12 min
• The Wiener filter and the orthogonality principle ~14 min
• The matched filter and signal detection ~12 min
• Cross-correlation for time-delay estimation ~10 min
• Linear prediction and all-pole modeling ~14 min
• The Karhunen-Loève transform ~12 min

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• Decimation, downsampling, and anti-aliasing ~12 min
• Interpolation, upsampling, and anti-imaging ~12 min
• Rational-factor sample-rate conversion ~12 min
• Polyphase decomposition and the noble identities ~12 min
• Half-band filters and interpolated FIR (IFIR) design ~12 min
• Two-channel filter banks: quadrature mirror filters and perfect reconstruction ~14 min
• Why multirate design is a systems-engineering trade-off ~10 min

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• Fixed-point, floating-point, and two's-complement number representation ~12 min
• The uniform quantization-noise model ~12 min
• Signal-to-quantization-noise ratio (SQNR) ~12 min
• Oversampled A/D and D/A conversion, noise shaping, and a first look at sigma-delta ~12 min
• Filter-coefficient quantization and pole/zero sensitivity ~12 min
• Limit cycles and overflow oscillation in fixed-point IIR filters ~12 min
• Finite-wordlength effects in FFT algorithms ~10 min
• What "no extensive math background" claims miss: calibrating this course's own difficulty honestly ~8 min

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• Recalling 1D convolution and the 1D DFT ~10 min
• 1D vs. 2D signals: an image as a 2D array ~10 min
• 2D convolution ~12 min
• 2D correlation ~12 min
• The 2D DFT and separability ~12 min
• Spatial aliasing and 2D downsampling ~12 min
• What a dedicated Digital Image Processing course adds ~14 min