Question

1.) Explain the difference between a time domain signal and a frequency domain signal.

2.) When would you select the frequency domain signal over the time domain signal.

Answer 1

1. Differences between time domain signal and frequency domain signal.

a. First of all, in nature, we rarely encounter a frequency domain signal. Almost all that occur in nature are time domain signals.

b. The frequency domain can be considered as the "transform domain" or "artificial domain". The purpose of transforming a time domain signal to frequency domain is due to the ease of processing in frequency domain to extract certain features.    The signal once processed can be brought back to time domain. Let us understand this by an example. Let us say we want to eliminate a background high frequency tone say 10 kHz, which crept in inadvertently, in an audio recorded speech (which is time domain). So first we transform the signal into frequency domain. Since audio recorded speech has much of the content in 10 Hz to 4 kHz, we band pass the signal using low pass filter of cut-off frequency 5 kHz(>4kHz) and eliminate the 10 kHz tone. Now we transform the signal back to time domain.

c. To transform "time domain" signal to "frequency domain" we use fourier transform (or varients such as dicrete fourier transform etc.) while to transform "frequency domain" to "time domain" we use inverse fourier transform.

d. Time domain signal can be plotted as signal amplitude against time while frequency domain signal is a plot of signal amplitude vs range of frequencies.

2. When would you select the frequency domain signal over the time domain signal

For ease of processing we migrate from time domain to frequency domain. In a research project that we are currently executing, we have have to transmit a message signal of 100 kHz signal using a carrier of 5.25GHz and receive it using another receiving antenna. What surprised us is though we could clearly see 100 kHz sine wave using our oscilloscope before transmission, after reception, no matter what, we could never observe a 100 kHz signal. The signal was corrupted by noise and the received signal in time domain did not seem to contain 100 kHz signal. However, after we used FFT to transform the received time domain signal to frequency domain, we could clearly see that there was a peak amplitude corresponding to 100 kHz. At all other frequencies 99 kHz, 98 kHz..down to 1 kHz..the amplitude of signal was hardly 10% of the peak signal noticed at 100 kHz.

So clearly when we use frequency domain signal over time domain signal is during the "processing stage". During signal generation and signal reception or at other times time domain signal is used.

Let me give an anology - if we try to answer the question when we use multiplication and when else do we use logarithms?. Logarithms is the transform domain to make multiplication simpler (by changing multiplication process to addition process). Similarly, frequency domain signals are used in the "processing stage" because they offer many advantages in way signal processing can be carried out.