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.
Category: Digital signal processing
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.
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 […]
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
