Hilbert Transform - real valued signal to a complex valued signal

[lucozade]

I'm reading text below that converts a real valued signal to a complex valued signal using a Hilbert Transform. The signal is the memory usage on a computer measured at 1 minute intervals. A discrete time Fourier analysis is then applied to do a frequency analysis.

My question is - why is it required to convert it to a complex valued signal? What are the benefits? Is it required to do a Fourier analysis?

Thanks

1. Frequency Analysis: We convert the real-valued telemetry signal into a complex-valued signal using the Hilbert
Transform:

H(x)

where (x) denotes the sample.

Following this transformation, we perform a discrete-time Fourier analysis to obtain the frequency-domain representation of the sampled windowed signal. This then allows us to obtain the power spectral density (PSD) of the signal. Using the PSD, we can then identify signal components by the frequency of their occurence via PSD analysis.

 

[axcdd]

Hilbert transform is widely use for getting lowpass equivalent of bandpass signal. All the hilbert transform does in frequency domain is multiply positive components by -j and negative ones by j. (It changes sinsoid components to cosinosid and vice-versa : so generally positive components are shifted by +90 deg while negative are shifted - 90 deg).

The only thing it does for PSD is that abs form negative components are attentuated and positive are multiplyed by 2. The same thing can be accomplished by plotting fft with signal length /2 +1 points in matlab.

maybe youre using hilbert because u got function writen that operates in complex values