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What is the relation between time-domain and frequency domain?
Parseval’s theorem gives the relationship between the squared integral of a time function and that of its Fourier transform, namely, the energy in the time domain is equal to the energy in the frequency domain.
How do you convert time-domain to frequency domain?
If we have a spectrum and want to look at the time-domain waveform, we simply take each frequency component, convert it into its time-domain sine wave, then add it to all the rest. This process is called the Inverse Fourier Transform.
What is time-domain amplitude?
The time domain display shows a parameter (usually amplitude) versus time. Frequency-domain displays show a parameter (again, usually amplitude) versus frequency. A spectrum analyzer takes an analog input signal—a time-domain signal—and uses the Fast Fourier Transform (FFT) to convert it to the frequency domain.
How are signals represented in the time domain?
In the time domain, signals can have any form. Passing into the frequency domain “work room,” signals are represented entirely by complex amplitudes.
What are the samples in the frequency domain?
The samples in the frequency domain are in general complex numbers; they represent coefficients that can be used in a weighted sum of complex exponential functions in the time domain to reconstruct the original time-domain signal. These complex numbers represent an amplitude and phase that is associated with each exponential function.
Why are impedances used in the frequency domain?
Because impedances depend only on frequency, we find ourselves in the frequency domain. A common error in using impedances is keeping the time-dependent part, the complex exponential, in the fray. The entire point of using impedances is to get rid of time and concentrate on frequency.
Which is Fourier transform maps time domain to frequency domain?
The discrete Fourier transform (DFT), commonly implemented by the fast Fourier transform (FFT), maps a finite-length sequence of discrete time-domain samples into an equal-length sequence of frequency-domain samples.