Enter your sequence and frequency into the calculator to determine the DTFT.

## Discrete-Time Fourier Transform (DTFT)

The Discrete-Time Fourier Transform (DTFT) is a fundamental concept in signal processing and systems analysis. It is used to analyze the frequency content of discrete-time signals. The DTFT converts a discrete-time signal into a continuous function of frequency, providing valuable insight into the spectral characteristics of the signal.

The DTFT is defined for a discrete sequence *x[n]* as follows:

X(e^{jω}) = Σ x[n] * e^{-jωn}

Where:

*X(e^{jω})*is the DTFT of the sequence*x[n]**ω*is the frequency variable*n*is the discrete time index*j*is the imaginary unit

## What is the Purpose of DTFT?

The DTFT is used to analyze and process signals in the frequency domain. By transforming a time-domain signal into its frequency components, engineers and scientists can study and manipulate the signal more effectively. This is particularly useful in fields such as telecommunications, audio processing, and control systems.

## How to Calculate DTFT?

The following steps outline how to calculate the DTFT of a discrete sequence:

- First, identify the discrete sequence
*x[n]*for which you want to compute