- #1
You need to show your work. It looks like you differentiated instead of integrated when calculating the coefficients.thecastlingking said:
A complex exponential Fourier series is a mathematical representation of a periodic function as a sum of complex exponential functions. It is used to decompose a periodic signal into its constituent frequencies, with each frequency represented by a complex coefficient.
The coefficients are calculated using the formula c_n = (1/T) * ∫f(t)e^(-jnω_0t)dt, where T is the period of the signal, n is the frequency index, ω_0 is the fundamental frequency, and f(t) is the periodic signal. This integral is evaluated over one period of the signal.
The coefficients represent the amplitude and phase of each frequency component in the original signal. They provide valuable information about the frequency content of a signal and are used in various applications such as signal filtering and compression.
Yes, the coefficients can be negative as they represent the amplitude and phase of a complex exponential function. The negative sign indicates a phase shift of π radians or 180 degrees.
Yes, there are a few limitations. The signal must be periodic and have a finite number of discontinuities. Also, the coefficients may not accurately represent signals with very high or very low frequencies, as they require an infinite number of coefficients to fully represent the signal.
