In the field of Digital Signal Processing (DSP), Fourier analysis is used to decompose the signals. The mathematical tool Discrete Fourier transform (DFT) is used to digitize the signals. The collection of various fast DFT computation techniques are known as the Fast Fourier transform (FFT). In simpler words, FFT is just an implementation of the … Read more
The field of digital signal processing or DSP includes the design and implementation of filters to filter the signals. These filters are mainly classified into two types depending on the duration of their impulse responses. They are known as infinite impulse response (IIR) filters and finite impulse response (FIR) filters. Let’s see the actual difference … Read more
A signal is a time-varying entity that carries some information from source to destination. Signals can be of many types such as electrical signal, sound signal, light signal, etc. In electronics, communication, and electrical engineering, we care about the electrical signals the most. For transmission of any other signals, we first need to convert them … Read more
In digital signal processing, the frequency-domain analysis of discrete-time signal is an important phenomenon to perform. This process includes the conversion of time-domain sequence to an equivalent frequency-domain representation. The tools Discrete Fourier transform (DFT) and Discrete-time Fourier transform (DTFT) are used in this conversion. DFT is the better version of DTFT as problems that … Read more
Laplace transform is a mathematical tool that converts a function of a real variable to a function of a complex variable s (complex frequency). It is used for solving differential equations. Here is the Laplace transform table. Laplace transform table S.No. Function Laplace transform 1. 1 \[\frac{1}{s}\] 2. eat \[\frac{1}{s-a}\] 3. e−at \[\frac{1}{s+a}\] 4. tn … Read more
A continuous-time signal is said to be a right-sided signal if there exists a T such that for all t < T, x(t) = 0. A discrete-time signal is said to be a right-sided signal if there exists a T such that for all n < T, x[n] = 0. A continuous-time signal is said … Read more
The energy of the continuous-time signal x(t) is given by Note: Here x(t) can be a real-valued signal or complex-valued signal. The energy of the discrete-time signal x(n) is given by Note: Here x(n) can be a real-valued signal or complex-valued signal. The power of the continuous-time signal x(t) is given by Note: Here x(t) … Read more
Conjugate symmetric Signal is a signal which satisfies the relation f(t) = f*(−t). It is also known as even conjugate signal. Example-1 f(t) = ejt f(−t) = ej(−t) f*(−t) = e(−j)(−t) = ejt = f(t) Hence, f(t) = f*(−t) Example-2 f(t) = ejωot f(−t) = ejωo(−t) f*(−t) = e(−j)ωo(−t) = ejωot = f(t) Hence, f(t) = f*(−t) … Read more
Even signal is a signal which satisfies the relation f(t) = f(−t). Even signal is symmetric about the y-axis. Example: cost. f(t) = cost f(−t) = cos(−t) = cost Hence, f(t) = f(−t) Odd signal is a signal which satisfies the relation f(t) = −f(−t). Odd signal is symmetric about the origin. Example: sinωt. f(t) = … Read more
Real valued signal is a signal which assumes a real value for its amplitude for all instants of time. Examples are, cosωot, rect(t), u(t), r(t), δ(t), eat (a is a real value). Complex valued signal is a signal which assumes a complex value for its amplitude atleast at one instant of time. Example is ejωot Since … Read more