**Digital Signal Processing using Scilab**

**A comprehensive tools for digital signal processing**

Scilab provides tools to visualize, analyze and filter signals in time and frequency domains.

**“ Teaching Signals and Systems using Scilab and its’ modules makes the students interested to explore more, event into most hatred DSP subjects!”**

**Course Synopsis**

Digital Signal Processing (DSP) is concerned with the digital representation of signals and the use of digital hardware to analyze, modify, or extract information from these signals. The rapid advancement in digital technology in recent years has created the implementation of sophisticated DSP algorithms that make real-time tasks feasible. A great deal of research has been conducted to develop DSP algorithms and applications.

Since DSP applications are algorithms that are implemented either on a processor or in software, a fair amount of programming is required. Using interactive software such as SCILAB it is now possible to place more emphasis on learning new and difficult signal processing concepts.

**Course Objectives**

This course provides an understanding of the DSP algorithms by including basic and advanced DSP concepts and also provides lab experiments on SCILAB to get insight into how the DSP algorithms work and to evaluate the performance of both simple and advanced DSP algorithms.

**Who Must Attend**

Engineer, technical support officers, and managers from the manufacturing, government and defense sectors who want to use or plan to use digital signal processing, to learn the fundamental knowledge in signal processing, to know how to use SCILAB for signal processing, or to be involved in the purchase of products that involve signal processing.

**Prerequisites**

Candidates must have experience with basic computer operation. Preferably attended our Numerical Computation with SCILAB & Signals and Systems with SCILAB course.

**Course Outline**

**Analog Signals and Systems in Time and Frequency Domains**

- Review of Analog Concepts
- Frequency domain representation of Complex Exponentials
- Fourier Series Representation
- Fourier Transform of non-periodic signals
- Magnitude and Phase Spectra
- Power and Energy Spectral Density
- Properties of Fourier Transform
- Linear and Time Invariant Systems
- Impulse Response and Its Significance
- Input – Output Relation: Convolution
- Stability Criterion
- Linear Constant Coefficient Differential Equations
- First-order and Second-order systems
- Frequency Response of a system
- Butterworth and Chebyshev Low Pass Filters
- Laplace Transform and Region of Convergence
- Properties of Laplace Transform

**Signal Sampling and Quantization**

- Sampling Theorem for Bandlimited signals
- Niquist Criterion
- Reconstruction of a signal from its samples
- Aliasing and nti-Aliasing Filter
- Quantization and Quantization Error
- Analog –to-Digital and Digital-to-Analog conversion
- Binary Representation of Quantized Signal
- Source Coding and Huffman Coding

**Discrete Signals and Systems in Time and Frequency domains**

- Basic Digital Signals and Classification
- Auto-Correlation and Cross-Correlation of Signals
- Fourier Transform of Discrete Signals
- Magnitude and Phase Spectrum for Digital Signals
- Linear and Time-Invariant Systems & Stability Criterion
- IIR and FIR Systems
- Realization of a Digital System using Direct Form-1 and Direct Form-2 methods.
- Recursive and Non-Recursive Systems
- Impulse Invariant Method and Bi-linear Transformation to transform a signal from Laplace domain to Z-domain.
- Frequency Transformations: LP to HP, BP, BS etc.

**Discrete Fourier Transform and Signal Spectrum**

- Discrete Fourier Series Coefficients
- Discrete Fourier Transform
- Amplitude Spectrum and Power Spectrum
- Spectral Estimation using Window Functions
- Fast Fourier Transforms (Decimation in Time and Decimation in Frequency)

**Complex Domain Representation of Digital Signals**

- Z-Transform and Properties
- Region of Convergence in Z plane
- Inverse Z-Transform
- Solution of Difference Equations using Z Transform

**Digital Processing Systems and Digital Filter Realizations**

- Difference Equations and Transfer Function
- System Function and Pole-Zero Diagram and Stability Criterion.
- Digital Filter Frequency Response.
- Classification and Realization of Digital Filters
- Tranformation of Analog Systems to Digital Systems
- Impulse Invariant Method and Bilinear Transformation Method

**Finite Impulse Response Systems**

- FIR System: Definition and Difference Equation
- FIR Filter Design: Fourier Transform Design & Window Method
- Frequency Sampling Method
- Realizations of FIR Systems: Transversal Form, Linear Phase Form, Lattice Structure
- Coefficient Accuracy Effects on FIR Filters

**Infinite Impulse Response Systems**

- IIR System: Definition and Difference Equation
- Digital Butterworth and Chebyshev Filter Design
- Higher order Infinite Impulse Response Filter Design using Cascade Method
- Pole-Zero Placement Method for IIR Filters

**DSP Implementation using SCILAB**

- Discrete time signal
- Unit sample sequence, Unit step sequence and Unit ramp sequence
- Even signal and Odd signal
- Z transform
- Convolution and Autocorrelation
- Fourier Transform and Continuous Time Fourier Transform
- Linear Filtering DFT
- Zero Padding
- Design of Filter
- Remez Algorithm Based
- Hilbert Transform
- Design of Filter: Analog to Digital
- IIR Filter Design Butterworth Filter
- Window Functions
- FIR Decimation and FIR Interpolation
- Sampling Rate Conversion Decimation
- Signal Distortion Ratio
- Sampling Rate Conversion Decimation Interpolation
- Wiener Filter