How to interpret complex DFT and FFT results?

How to interpret complex DFT and FFT results?

Key focus: Interpret FFT results, complex DFT, frequency bins, fftshift and ifftshift. Know how to use them in analysis using Matlab and Python. Often, one is confronted with the problem of converting a time domain signal to frequency domain and vice-versa.

Where does fftshift put the Nyquist frequency in the spectrum?

FFTshift shifts the DC component to the center of the spectrum. It is important to remember that the Nyquist frequency at the (N/2+1)th Matlab index is common to both positive and negative frequency sides. FFTshift command puts the Nyquist frequency in the negative frequency side. This is captured in the following illustration.

How is the amplitude of the FFT related to its magnitude?

The FFT returns a two-sided spectrum in complex form (real and imaginary parts), which you must scale and convert to polar form to obtain magnitude and phase. The frequency axis is identical to that of the two-sided power spectrum. The amplitude of the FFT is related to the number of points in the time-domain signal.

Is the FFT length sufficient to cover the entire length of the signal?

Lets consider taking a point FFT, which is the power of . Note: The FFT length should be sufficient to cover the entire length of the input signal. If is less than the length of the input signal, the input signal will be truncated when computing the FFT.

How to get the DTFT from the DFT samples?

In the DTFT the index n extends to ± ∞, even if the function x [n] is non-zero over a finite length. Adding zeros to the DFT is adding more of these zero samples, so interpolates samples on the DTFT. As n extends approaches infinity in the limit, the resulting function becomes continuous (the DTFT).

How to calculate the frequency of a discrete signal?

Harmonic discrete signals (harmonic sequences) x[n] = C1 cos(ω1n+φ1) (1) • C1 is a positive constant – magnitude. • ω1 is a spositive constant – normalized angular frequency. As n is just a number, the unit of ω1 is [rad].

Can a time domain signal be synthesized from DFT pairs?

The real-valued time domain signal can be synthesized from the real DFT pairs as Caveat: When using the synthesis equation, the values and must be divided by two. This problem is due to the fact that we restrict the analysis to real-values only.

What do the DFT coefficients of a DFT mean?

At it’s most fundamental, the DFT is about fitting a set of basis functions to a given set of sampled data. The basis functions are all sinusoidal functions, expressed as the complex exponential with a purely imaginary exponent. Using the most common scaling convention each basis function, without its scaling coefficient, is:

Why is DTFT not suitable for DSP applications?

Discrete Fourier Transform (DFT) Recall the DTFT: X(ω) = X∞ n=−∞ x(n)e−jωn. DTFT is not suitable for DSP applications because •In DSP, we are able to compute the spectrum only at specific discrete values of ω, •Any signal in any DSP application can be measured only in a finite number of points. A finite signal measured at N points: x(n) =

What do we mean by FFT, Fast Fourier transform?

By fft, Fast Fourier Transform, we understand a member of a large family of algorithms that enable the fast computation of the DFT, Discrete Fourier Transform, of an equisampled signal. A DFT converts a list of N complex numbers to a list of N complex numbers, with the understanding that both lists are periodic with period N.

Which is the oversampling factor in FFT function?

I have chosen a oversampling factor of so that the sampling frequency will be , and that gives samples in a seconds duration of the waveform record. Lets represent the signal in frequency domain using the FFT function. The FFT function computes -point complex DFT.

How is the FFT used in signal analysis?

Computations Using the FFT The power spectrum shows power as the mean squared amplitude at each frequency line but includes no phase information. Because the power spectrum loses phase information, you may want to use the FFT to view both the frequency and the phase information of a signal.

How to interpret FFT results in MATLAB ebook?

Wireless Communication Systems in Matlab, ISBN: 978-1720114352 available in ebook (PDF) format (click here) and Paperback (hardcopy) format (click here). Consider a cosine signal of amplitude , frequency and phase radians (or )