Discrete Fourier Transform

This applet takes a discrete signal \(x[n]\), applies a finite window to it, computes the discrete-time Fourier transform (DTFT) of the windowed signal and then computes the corresponding discrete Fourier transform (DFT). The results are shown graphically in three plots.

The left hand plot shows \(x[n]\) in white. This is a mixture of two discrete-time sinusoids. The formula for \(x[n]\) is shown above the plot. The amplitudes and frequencies of the sinusoids are set using the sliders below the plot.

The center plot has two views of the window and windowed signal. You choose the view using the "View time" and "View frequency" radio buttons below the plot. The length and shape of the window are set with controls below the plot.

In the time view, the plot shows the window, \(w[n]\), in blue and the windowed signal, \(x_w[n] = w[n]x[n]\) in white.

In the frequency view the magnitude of the DTFT of the window, \(|W(f)|\), is shown in blue.

The right hand plot shows the magnitude of the DTFT of the windowed signal in white. The magnitude of the DFT (i.e. samples of the DTFT) is shown with green dots. The number of points in the DFT is set using the control below the plot.

The two horizontal "Zoom" sliders control the horizontal scales in the center and right hand plots. A common vertical "Zoom" slider controls the vertical scale of both plots. You can separately set the center of these plots by dragging them with your mouse.

The "Save plot" button saves the current plot. After clicking this, the saved \(x[n]\), \(x_w[n]\) and \(|X_w(f)|\) are shown in orange and the saved \(w[n]\) in dark orange. In the frequency view, the center plot shows the saved \(|W(f)|\) in dark orange. The "Clear saved plot" button removes the saved plot from all three plots.