**1. Discrete Time Signal**

- Introduction to Digital Signal Processing, Discrete Time Signals,
Sampling and Reconstruction, Standard DT Signals, Concept of Digital
Frequency, Representation of DT signal using Standard DT Signals,
Signal Manipulations(shifting, addition, subtraction, multiplication),
Classification of Signals, Linear Convolution formulation(without
mathematical proof), Circular Convolution formulation(without
mathematical proof), Matrix Representation of Circular Convolution,
Linear by Circular Convolution. Auto and Cross Correlation formula
evaluation,

**2. Discrete Time System**

- Introduction to Discrete Time System, Classification of DT Systems
(Linear/Non Linear, Causal/Non Causal, Time Invariant/Time Variant
Systems, Stable/ Unstable), BIBO Time Domain Stability Criteria. LTI
system, Concept of Impulse Response and Step Response.
- Concept of IIR System and FIR System, Output of IIR and FIR DT
system using Time Domain Linear Convolution formula Method.

**3. Discrete Fourier Transform**

- Introduction to DTFT, DFT, Relation between DFT and DTFT, Properties
of DFT without mathematical proof (Scaling and Linearity, Periodicity,
Time Shift and Frequency Shift, Time Reversal, Convolution Property
and Parsevals’ Energy Theorem). DFT computation using DFT properties.
- Transfer function of DT System in frequency domain using DFT. Linear
and Circular Convolution using DFT. Response of FIR system calculation
in frequency domain using DFT.

**4. Fast Fourier Transform**

- Radix-2 DIT-FFT algorithm, DIT-FFT Flowgraph for N=4, 6 & 8, Inverse
FFT algorithm. Spectral Analysis using FFT, Comparison of complex and
real, multiplication and additions of DFT and FFT.

**5. DSP Algorithms**

- Carls’ Correlation Coefficient Algorithm, Fast Circular Convolution
Algorithm, Fast Linear Convolution Algorithm, Linear FIR filtering
using Fast Overlap Add Algorithm and Fast Overlap Save Algorithm,

**6. DSP Processors and Application of DSP**

- Need for Special architecture of DSP processor, Difference between DSP
processor & microprocessor, A general DSP processor TMS320C54XX
series, Case study of Real Time DSP applications to Speech Signal
Processing and Biomedical Signal Processing.