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Foundations of Digital Signal Processing
1. Review of discrete-time signals and systems
1.1. Discrete-time signals
1.2. Discrete-time systems
1.3.
\(z\)
-Transform
2. Fourier (Frequency Domain) Analysis
2.1. Discrete-Time Fourier Transform (DTFT)
2.2. DTFT properties and tables
2.3. Periodic Dirac delta
2.4. DTFTs of infinite-energy signals
2.5. Fourier Series
2.6. Continuous-Time Fourier Transform (FT)
2.7. Dirac delta and FTs of infinite-energy signals
3. Sampling and Reconstruction
3.1. Poisson Sum Formula
3.2. Sampling Theorem
4. Time-dependent Fourier Analysis
4.1. Uncertainty Principle
4.2. Short-time DTFT
5. Computation of Fourier Analysis
5.1. Frequency-domain Sampling
5.2. Discrete Fourier Transform
5.3. Fast Fourier Transform
5.4. Linear Filtering with FFT
6. Filter Design
6.1. Frequency Response of LTI System
6.2. Pole-Zero Placement
6.3. Allpass Filter
6.4. Minimum-phase Filter
6.5. Linear-phase Filter
6.6. FIR Filter Design
6.7. IIR Filter Design
7. Multi-rate Processing
7.1. Downsampling
7.2. Interpolation
7.3. Rational Rate Conversion
7.4. Multi-rate Filtering
7.5. Polyphase Decomposition & Related Identities
7.6. Polyphase Implementation of Downsampling
7.7. Polyphase Implementation of Interpolation
7.8. Polyphase Implementation of
\(\frac{U}{D}\)
-rate Filter
8. References
Repository
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Computation of Fourier Analysis
5.
Computation of Fourier Analysis
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