DFT of a cosine/sine wave?

1. What is DFT of cosine?
2. What is the FFT of a sine wave?
3. How is DFT calculated?
4. How do you calculate DFT frequency?

What is DFT of cosine?

The Discrete Fourier Transforms (DFTs) of cosine and sine waves have particularly simple analytical expressions. The transform. Properties of trigonometric functions and complex exponentials. DFT of a cosine wave with integer frequency.

What is the FFT of a sine wave?

The FFT. The function fft( ) estimates the coefficients of the Fourier transform, transforming a time-domain signal (i.e., an observed fMRI time series) into a series of sine waves with different amplitudes and phases. Fourier coefficients are complex numbers, with values in the real and imaginary planes.

How is DFT calculated?

The DFT formula for X k X_k Xk​ is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk​=x⋅vk​, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .

How do you calculate DFT frequency?

calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im) find the bin with the largest magnitude, call its index i_max . calculate the equivalent frequency of this bin: freq = i_max * Fs / N , here Fs = sample rate (Hz) and N = no of points in FFT.