Discrete Fourier Transform -- Help

 

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 a 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 discrete time signal which is a mixture of two 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 checkboxes 'View time' and 'View frequency' at the bottom of the window below the plot. The length and type 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, xw[n] = w[n]x[n] in white.

In the frequency view the magnitude |W(f)| of the DTFT of the window 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. the sampled DTFT) is shown with green dots. The number of points in the DFT is set using the 'DFT length' slider.

The two 'Zoom' sliders control the vertical and horizontal scales in the right hand plot. You can set the center of the right hand plot by dragging the graph withy our mouse.

The vertical 'Zoom' slider also controls the vertical scale of the center plot in frequency view.

The 'Save plot' button saves the current plot. After clicking this the saved x[n], xw[n] and |Xw(f)| will be shown in yellow. In the frequency view, the center plot will show the saved |W(f)| in light blue. The 'Clear saved plot' button removes the saved plot from the all three plots.

 

©2011 J. Greenberg, H. Miller, J. Orloff, J.-M. Claus