distortion Archives

In Problem 4.36 of DSP-Proakis [1], the task is to provide insights into harmonic distortion which may be present in practical sinusoidal generators. Consider the signal
$x(n) = \cos(2\pi f_0 n)$ , where $f_0 = k_0/N$ .

My take:
The discrete time signal of fundamental period $N$ can consist of frequency components separated by $2\pi/N$ radians or $f =1/N$ cycles (Refer Section4.2 in [1]).

The Fourier series coefficient at frequency $f_0$ is,
$c_{k0} = \frac{1}{N}\sum_{n=0}^{N-1}x(n)e^{\frac{-j2\pi k_0 n}{N}}$ .

The total power of the signal over a period $P_x$ is same as the sum of the power of all the Fourier series coefficients (harmonic components) i.e.
$P_x = \frac{1}{N}\sum_{n=0}^{N-1}|x(n)|^2 = \sum_{k=0}^{N-1}|c_k|^2$ .

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