# Is DTFS and DFS same?

## Is DTFS and DFS same?

i think mainly u know the difference between DTFS and DTFT. now coming to DTFS and DFS the difference is that you apply DTFS to a periodic signal and DFS to a finite discrete signal which is not periodic but made periodic by adding some values.

### How do you do DTFT in Matlab?

1. function [X] = dtft(x,n,w)
2. % Computes Discrete-time Fourier Transform.
3. % [X] = dtft(x,n,w)
4. % X = DTFT values computed at w frequencies.
5. % x = finite duration sequence over n.
6. % n = sample position vector.
7. % w = frequency location vector.
8. X = exp(-1i*w’*n) * x. ‘;

#### What is DFT in Matlab?

The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. The foundation of the product is the fast Fourier transform (FFT), a method for computing the DFT with reduced execution time.

How do I find the DFT of an image in Matlab?

Compute the two-dimensional DFT of A and B using the fft2 function. Multiply the two DFTs together and compute the inverse two-dimensional DFT of the result using the ifft2 function. C = ifft2(fft2(A). *fft2(B));

What is DFS and DFT?

The discrete Fourier series (DFS) is used to represent periodic time functions and the DFT is used to repre- sent finite-duration time functions.

## What is DFT in DSP?

The discrete Fourier transform (DFT) is one of the most important tools in digital signal processing.

### How do you code DFT?

Then the basic DFT is given by the following formula: X(k)=n−1∑t=0x(t)e−2πitk/n. The interpretation is that the vector x represents the signal level at various points in time, and the vector X represents the signal level at various frequencies.

#### Why is DFT used?

Applications of the DFT First, the DFT can calculate a signal’s frequency spectrum. This is a direct examination of information encoded in the frequency, phase, and amplitude of the component sinusoids. For example, human speech and hearing use signals with this type of encoding.

What is difference between DFT and FFT?

FFT is an implementation of the DFT used for used for fast computation of the DFT. In short, FFT can do everything a DFT does, but more efficiently and much faster than a DFT. It’s an efficient way of computing the DFT.

What is the difference between DTFT and DTFS?

Relationship between DTFS and DTFT: The DTFS is simply a special case of the DTFT for periodic functions. If a function x[n] is periodic, its DTFT consists only of impulses occurring at K/N0 with strengths X[K].

## What is the difference between Z transform and DFT?

The principal difference between the Z and the discrete time fourier transform is that, the DTFT is a derived of the Z transform, because, in the Z transform, Z means a complex number (Ae^(Θ)) with any magnitude and any phase angle, but in the DTFT, this complex number is restricted to an only magnitude, A must be only …

### Why DFT is used?

#### What is DFT explain briefly?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

What is DFT formula?

The DFT formula for X k X_k Xk​ is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk​=x⋅vk​, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .

Why FFT is used over DFT?

The Fast Fourier Transform (FFT) is an implementation of the DFT which produces almost the same results as the DFT, but it is incredibly more efficient and much faster which often reduces the computation time significantly. It is just a computational algorithm used for fast and efficient computation of the DFT.