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Course overview
This course covers digital signal processing from discrete-time signal fundamentals through to filter design and multirate processing. Students begin by reviewing discrete-time signals and systems, then work through the DFT and its efficient computation via the FFT. FIR filter design using window methods and frequency sampling follows, after which students learn IIR filter design via bilinear transformation. The final module covers multirate DSP concepts. After completing the course, students can implement and analyze FIR and IIR filters, compute the DFT manually and using the FFT butterfly structure, and understand decimation and interpolation.
Details
Target audience: Third-year B.Tech ECE students taking DSP as a core course, and GATE aspirants who need a focused review of the DSP section.
Duration: 12 to 15 hours across 5 modules
Prerequisites
- Discrete-time signals and Z-transform from Signals and Systems
- Complex number arithmetic and Euler's formula
- Basic filter concepts: passband, stopband, and cutoff frequency
Learning outcomes
- Compute the N-point DFT of a given sequence by hand and verify symmetry properties for real inputs
- Perform circular convolution using the DFT and relate it to linear convolution with zero-padding
- Trace the radix-2 DIT FFT butterfly diagram for an 8-point or 16-point sequence
- Design FIR low-pass filters using the rectangular and Hamming window methods for a given cutoff frequency
- Design IIR Butterworth low-pass filters using the bilinear transformation and verify the frequency response
- Apply decimation and interpolation operations and identify the required anti-aliasing and anti-imaging filters
Modules
- Discrete-time signal representation and classification
- Linear convolution and correlation
- Z-transform review and system function
- Frequency response of discrete-time systems
- Sampling theorem and aliasing
- DFT definition and computation for N-point sequences
- Inverse DFT and circular shift property
- Circular convolution and its relationship to linear convolution
- Overlap-add and overlap-save methods
- DFT of real sequences and spectral symmetry
- Radix-2 DIT FFT butterfly structure
- Radix-2 DIF FFT and bit-reversal permutation
- Computational complexity: N log2 N versus N squared
- Inverse FFT using the FFT algorithm
- FFT applied to fast convolution
- FIR filter design using rectangular, Hamming, and Kaiser windows
- Frequency sampling design method for FIR filters
- Analog prototype filters: Butterworth and Chebyshev
- IIR design via bilinear transformation
- Comparison of FIR and IIR filter properties
- Decimation by factor M: downsampling and anti-aliasing filter
- Interpolation by factor L: upsampling and anti-imaging filter
- Polyphase decomposition for efficient filter implementation
- Sampling rate conversion by rational factor L/M
- Introduction to filter banks and subband coding