Digital Signal Processing with MATLAB Implementation

In this article, we explore fundamental concepts of Digital Signal Processing with practical MATLAB implementations. The discussion covers convolution techniques including time-domain convolution (timeconv) for direct computation, time-domain circular convolution (timecirconv) using periodic extension, frequency-domain convolution (freqconv) via FFT multiplication, frequency-domain circular convolution (freqcirconv), and the overlap-save method (dupconv) for efficient block processing. For frequency domain analysis, we examine radix-2 FFT implementation (d2fft) using butterfly operations, simplified DFT computation (dft) with matrix multiplication approaches, and DTFT demonstration (dtft) for continuous frequency analysis. The FIR filter design section includes methods to obtain filter coefficients (fir) using windowing techniques, window function generation (getwindow) for various window types (Hamming, Hanning, etc.), and ideal filter design (idealfilter) for lowpass, highpass, and bandpass filters (hdn) with frequency specification parameters. Additionally, we cover signal generation techniques for creating discrete-time signals with proper sampling and quantization considerations. Each concept includes MATLAB code explanations focusing on algorithmic implementation, key functions, and practical application scenarios to enhance understanding of DSP fundamentals.