Fourier series coefficients of a rectangular pulse signal

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Fourier series coefficients of a rectangular pulse signal

April 12 2009 compiled on — Wednesday July 06, 2016 at 08:31 AM

This demonstration calculates and plots the magnitude and phase of the Fourier coefficients for a rectangular pulse train signal. A rectangular pulse is defined by its duty cycle (the ratio of the width of the rectangle to its period), and by the delay of the pulse. In this demonstration, the pulse period is fixed at one second, and the height is fixed at unity.

The delay and the duty cycle can be adjusted as well as the number of Fourier coefficients. We notice that, since the signal is a real signal, the magnitude plot is an even function and the phase plot is an odd function.

The $th n$ Fourier coefficient of a rectangular pulse train is given by

2π cn = hd sinc(nd)e−ITont0

Where $h$ is the pulse height, $d$ is the duty cycle, $T0$ is the period of the pulse train, $t0$ is the delay of the pulse in seconds. $sinc$ is defined as $sin(πx)- πx$ .

This demonstration displays the magnitude and phase of $c n$ .