# Digital Signal Processing Course (DSP) – Learn from scratch

Course content

## What is digital signal processing (DSP)? – A complete overview

An introduction to Digital Signal Processing that includes everything you need to know about the DSP, its merits and demerits, and its applications.

## Overview of Signals and Systems – Types and differences

This is a revision post to help you brush up on your knowledge of the different types of elementary signals, their graphs, and equations. We’ll also talk about other different types of signals and systems and differentiate them to bring you up-to-speed quickly. Just breeze through this one because you’ll be needing the info in the rest of this Digital Signal Processing course.

## A simple explanation of the signal transforms (Laplace, Fourier and Z)

Can’t understand Fourier or Laplace or Z signal transforms? This is the easiest way to understand what they are, how they relate with each other and what’s their purpose.

## What is aliasing in DSP and how to prevent it?

Aliasing is a very common undesirable effect in the processing of digital signals. In this post, we discuss what it is, its implications and how to avoid it.

## Convolution – Derivation, types and properties

Convolution is an important operation in digital signal processing. In this post, we will introduce it, derive an equation and see its types and properties.

## What is the difference between linear convolution and circular convolution?

There are two types of convolution. Linear convolution and circular convolution. Turns out, the difference between them isn’t quite stark.

## Discrete Time Fourier Transform (DTFT) vs Discrete Fourier Transform (DFT)

The Discrete Fourier Transform is a subset of the Discrete Time Fourier Transform. But there are some subtle differences between the two. Let’s check em out

## Twiddle factors in DSP for calculating DFT, FFT and IDFT

An easy to understand summary of twiddle factors, their usage in calculating DFT and IDFT in DSP and their cyclic properties.

## Properties of DFT (Summary and Proofs)

These properties of the discrete Fourier transform are used to simplify calculations. Let’s take a quick look at them & go on to prove them mathematically.

## Computing Inverse DFT (IDFT) using DIF FFT algorithm – IFFT

For the faster calculation of inverse DFT (IDFT) we can use Decimation in Frequency (DIF) Fast Fourier Transform (FFT) with the butterfly diagram.

## Region of Convergence, Properties, Stability and Causality of Z-transforms

A simple explanation and summary of all the properties of the ROC of a Z-transform. We will also discuss the conditions for the stability & causality of the Z-transform.

## Z-transform properties (Summary and Simple Proofs)

There are some properties of the z-transform that can be used to simplify calculations. Let’s take a quick look at them & go on to prove them mathematically

## Relation of Z-transform with Fourier and Laplace transforms – DSP

The relationship between the z transform and laplace and fourier transforms is important for the designing of a digital filter. Let’s derive it.

## What is an Infinite Impulse Response Filter (IIR)?

One of the two main digital filter types, the Infinite Impulse Response (IIR) filter is a major part of any DSP curriculum. Let’s take an in-depth look into what it is.

## Approximation of derivatives method to design IIR filters

The backward difference method (aka approximation of derivates method) is one of the main ways to get a digital IIR filter from an analog filter.

## Impulse invariance method of IIR filter design

This is the second method that we will be studying to design a digital IIR filter from an analog filter. We will also take up an example problem to highlight the steps to take to use this method. The Impulse Invariance method has its back draws too and we will address that in the next post.

## Bilinear transform method of designing IIR filters

This is the third method that we’ll see to design IIR filters. It is an improved technique over Impulse invariance and Approximation of derivatives. Let’s study about it along with a look at all the derivations, advantages, and the pre-warping technique to overcome its solitary disadvantage.

## Difference between Infinite Impulse Response (IIR) & Finite Impulse Response (FIR) filters

IIR vs FIR is an evergreen distinction in DSP. Both these filter types have their advantages and disadvantages & you’ll need to know them to make a choice.

## Ideal Filter Types, Requirements, and Characteristics

The ideal filter is the dream for signal processing engineers. To get those sexy clean-cut waveforms is like hitting a jackpot. Naturally, ideal filters are something we wish to emulate. To emulate them, we have to try to understand everything there is about them. Let’s get warmed up to all the different types of ideal filters, their properties, waveforms, and characteristics. We’ll also discuss how we can get as close to them as possible using different approximation techniques.

## Filter Approximation and its types – Butterworth, Elliptic, and Chebyshev

We can’t really get our hands on an ideal filter. However, we can get close to the parameters of an ideal filter. These three methods: Butterworth, Elliptic, and Chebyshev offer us three filters that come close to some of the parameters of an ideal filter. Check them out. They are pretty important in Digital Signal Processing.

## Butterworth Filter Approximation – Impulse Invariance & Bilinear Transform

As discussed in the post on ideal filter types, the Butterworth filter is a filter approximation technique that is also known as the maximally flat filter technique. This filter gives a very flat frequency response in the Pass Band, which ensures that there are no ripples present. Hence, as the name suggests, the maximal flat […]

## Fourier series method to design FIR filters

We can use the concepts of Fourier series to design FIR filters by applying the methods to the frequency response of the filters we desire. Though it is short and easy to understand, this method comes with the back draw of Gibb’s phenomena.

## Windowing Method to design FIR filters

The windowing method is a very simple way of designing digital FIR filters. All we have to do is find the right window according to our requirements and “push” an IIR filter through it. In this post, we’ll discuss the purpose of windowing, types of windows, and all the designing steps involved.

## Quantization of filter coefficients in digital filter design

The practical designing of filters requires the coefficients of the filter’s transfer equation to be quantized. Let’s see how the quantization is acheived.

## Quantization in DSP – Truncation and Rounding

Rounding and Truncation are two easy methods to quantize a filter coefficient in digital signal processing. Let’s see a simple explanation of the two.

## Limit Cycle Oscillation in recursive systems

Limit cycle oscillations are an unwanted implication of finite-word length effects in an IIR filter. These arise due to inherent system quantizations.

## Digital Signal Processing Quiz | MCQs | Interview Questions

This DSP quiz is crafted to test your skills in the fundamental concepts of digital signal processing taught in this course. Upon clearing this quiz, you will gain access to the final certification quiz. Please ensure that you are signed in before attempting the quiz.

More details

New posts are still being added to this course.

### What will you learn in this course?

• Learn various transform techniques for the analysis of time-domain and frequency-domain signals (Laplace transform, DFT, Z-transform, etc.)
• System impulse response calculation techniques
• Conduct frequency domain analysis of signals
• Understand the behavior of linear time-invariant systems
• Identify and design digital filters
• Design methods and analysis of IIR filters
• Design methods and analysis of FIR filters
• Structures to realize digital filters

MATLAB

### What is the target of this course?

This course is part of the Communications and Signal processing track. We have designed this track and its constituent courses to equip learners with the basic requirements of entry-level jobs or internships in the field of communication and signal processing.

### Are there any pre-requisites for this course?

• Advanced calculus and complex variable theory.
• Fourier, Laplace, and Z transform.
• Signals and Systems

### What’s the course structure like?

• Digital Signal Processing –Introduction, Systems, Advantages, and Applications.
• Elementary discrete-time signals: Unit sample, unit step signal, unit ramp signal, and exponential signal.
• Fourier signals and Fourier transform of signals.
• Convolution of signals.
• Correlation of signals.
• Z transform of digital signals.
• Types and properties of Z transform.R
• Relationship between Z transform and Laplace Transform.
• Relationship between Fourier transform and Z transform.
• Discrete Fourier Transform (DFT) – Linear transform and properties
• Circular convolution and Linear Convolution
• Fast Fourier Transform (FFT)
• Decimation in frequency (DIF) algorithm and Decimation in Time (DIT) algorithm.
• Computation of inverse DFT using FFT.
• Fast Convolution – Overlap-add and Overlap-save methods.
• Infinite Impulse Response Filter (IIR) – Butterworth, Chebyshev, and Elliptic.
• Finite Impulse Response Filter (FIR) – Design and Gibbs phenomenon.
• Design techniques for FIR filters – Fourier series, frequency sampling, and window method.
• Finite Word Length Effect in Digital Filters – Quantization, product quantization error.

### I would like to suggest some topics to be covered, how can I do that?

You can visit the contact page linked in the footer of this webpage. Just select “Suggest Topics” from the subject dropdown menu of the form, mention the course and why you think your suggestion makes sense to be part of the curriculum.

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