Contents
Is the real part of the spectrum the same as complex FFT?
For the case of the complex FFT, the real part of the spectrum is the same but the imaginary part of the spectrum represents the contribution from the sinusoid basis function. Does this mean different (more?) information is present in the complex FFT as it includes information about the phase of the signal?
What are the two parts of a complex signal?
A complex signal consists of two real signals – one for the real and one for the imaginary part. The linear processing of a complex signal, such as filtration with a time-invariant linear filter, corresponds to applying the processing both to the real and the imaginary part of the signal.
How is the complex signal x ( t ) written?
Notice that all real, imaginary, and neither real nor imaginary signals are complex A complex signal x (t) can be written in the form x (t) = a (t) + \\jmath b (t), where a (t) and b (t) are real signals
Which is a real signal and an imaginary signal?
Real A real signal is a complex signal x(t) = a(t) + jb(t) where b(t) = 0 Imaginary A (pure) imaginary signal is a complex signal x(t) = a(t) + jb(t) where a(t) = 0 Examples Complex, but not purely real nor imaginary
Is the FFT based on the complex DFT?
The FFT is based on the complex DFT, a more sophisticated version of the real DFT discussed in the last four chapters. These transforms are named for the way each represents data, that is, using complex numbers or using real numbers.
How many real numbers do you need for FFT?
If you throw away the phase information, that could easily massively distort the signal if you try to recreate it using an iFFT (and the signal isn’t symmetric). So a complete FFT result requires 2 real numbers per FFT bin.
Which is the real part of the DFT signal?
The real DFT transforms an N point time domain signal into two N /2 + 1 point frequency domain signals. The time domain signal is called just that: the time domain signal. The two signals in the frequency domain are called the real part and the imaginary part, holding the amplitudes of the cosine waves and sine waves, respectively.