Discrete Fourier series of an odd signal

1. How do you know if a Fourier series is even or odd?
2. What is the DFT of imaginary and odd signal?
3. What is DSP odd signal?
4. What is odd signal formula?

How do you know if a Fourier series is even or odd?

4.6 Fourier series for even and odd functions

A function is called even if f(−x)=f(x), e.g. cos(x). A function is called odd if f(−x)=−f(x), e.g. sin(x).

What is the DFT of imaginary and odd signal?

Similarly, if a signal is odd and real, then its DTFT is odd and purely imaginary. This follows from Hermitian symmetry for real signals, and the fact that the DTFT of any odd signal is imaginary.

What is DSP odd signal?

Odd Signal:

A signal is odd if x(t) = -x(-t). An odd signal must be 0 at t=0, in other words, odd signal passes. the origin.

What is odd signal formula?

Hence, 𝑥(𝑡) ≠ 𝑥(−𝑡); but 𝑥(−𝑡) = −𝑥(𝑡), thus the given signal is an odd signal. Therefore, 𝑥(𝑡) = 𝑥(−𝑡) and 𝑥(−𝑡) ≠ −𝑥(𝑡), thus the given signal is an even signal.