Digital Signal Processing with MATLAB (Codes Included)

Explore digital signal processing fundamentals from sequences and z transforms to transfer functions, and learn to design and implement finite and infinite impulse response filters using MATLAB.

Master digital signal processing with Matlab by exploring digital signals, linear shift invariant systems, representations via difference equations, block diagrams, signal flow graphs, and convolution and filter design.

Explore how convolution and sampling define digital signal processing, using flip and shift to obtain outputs from input sequences through an impulse response in linear shift invariant systems.

Explore how sampling converts continuous signals to digital form via adcs and dacs. Use Nyquist to sample at least twice the highest frequency to avoid aliasing.

Learn Matlab basics: navigate the main window, use the command window and workspace, create and edit scripts, build arrays, plot sequences, and customize plots.

Explore transforming digital signals from time domain to frequency domain, inspect frequency content, and leverage multiplication in the frequency domain for efficient convolution.

The lecture compares time-domain convolution with a frequency-domain approach by multiplying the signals' frequency-domain representations. Reversing the transform yields the same time-domain output.

Demonstrate how the discrete Fourier transform reveals frequency content via the real and imaginary parts, magnitude, and phase, and how zero padding enables linear convolution.

Explore z transform as a generalization of the discrete Fourier transform, evaluated across the complex plane. Relate transfer functions to poles and zeros and assess stability via unit circle.

Design and implement digital filters by defining passband, stopband, corner frequencies, and filter order; compare low pass, high pass, bandpass, and notch filters with ideal and practical responses.

Explore digital filters, focusing on infinite impulse response design using analog prototypes and the bilinear (tustin) transform, with prewarping to compensate frequency warping and address stability and resource considerations.

Compare infinite and finite impulse response filters, noting stability, feedback, and resource use. Use analog design with bilinear (Tustin) transform and pre-warping to obtain stable digital filters.

Design finite impulse response filters with windowing in MATLAB, comparing rectangular, Hamming, and Blackman windows, and outline steps to create a causal, efficient filter.

Design an impulse response FIR filter at 100 kHz with a 20 kHz passband and 40 kHz stopband, comparing Hamming and Blackman windows for 40 dB attenuation and low ripple.

Learn how to implement digital filters in software by converting transfer functions and impulse responses into difference equations, and implement IIR and FIR filters in MATLAB.

Observe real-world filter implementation in MATLAB, using a Butterworth low-pass transfer function translated to digital, then test with two sine waves to compare input and output frequency responses.

Explore designing an IIR Butterworth filter in Matlab, deriving transfer function coefficients and converting to a digital system with c2d at 40 kHz, validating with Bode plots.