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Digital and analog signal processing
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Module 4
From Analog to Digital: Sampling and Reconstruction
1
From Nyquist to Shannon: A History of Sampling Theory
Trace the historical development of sampling theory from Nyquist's work to Shannon's formulation.
2
Deriving the Sampling Theorem from Impulse Sampling
Derive the sampling theorem by analyzing the spectrum of an impulse-sampled continuous-time signal.
3
Understanding Aliasing: Mathematical Analysis and Reconstruction Conditions
Analyze the phenomenon of aliasing mathematically and derive the conditions for alias-free signal reconstruction.
4
Ideal Reconstruction with Sinc Interpolation
Derive the ideal reconstruction formula using a lowpass (sinc) interpolation filter.
5
Anti-Aliasing & Reconstruction Filters: Necessity and Design
Explain the practical necessity and design considerations for anti-aliasing and reconstruction filters.
6
Relating Continuous and Discrete Frequencies
Derive the relationship between continuous-time frequency (Ω) and discrete-time frequency (ω).
7
Bandpass Sampling Theorem: Derivation and Application
Derive and apply the bandpass sampling theorem for efficient sampling of band-limited signals.
Previous module
Analog Filter Design Principles
Next module
Discrete-Time Signals and Systems in the z-Domain