Contents
How does the frequency of a sine wave affect its phase?
Frequency is commonly measured in Hertz, or cycles per second. So frequency x time = (cycles/sec) x sec = # of cycles. Thus two sine waves differing in frequency by 200 Hz get progressively out of phase with each other by 200 cycles every second.
What does the frequency-domain tell us?
Frequency domain is an analysis of signals or mathematical functions, in reference to frequency, instead of time. Also, a frequency-domain representation can include information on the phase shift that must be applied to each sinusoid to be able to recombine the frequency components to recover the original time signal.
Why do we use frequency-domain?
The frequency domain representation of a signal allows you to observe several characteristics of the signal that are either not easy to see, or not visible at all when you look at the signal in the time domain. For instance, frequency-domain analysis becomes useful when you are looking for cyclic behavior of a signal.
What is the relationship between time and frequency of a sine wave?
The period T is the reciprocal of a frequency, T = 1 / f. The period of a waveform is the time required for one complete cycle of the wave to occur. The relationship between period, frequency, and amplitude for a sine wave is illustrated in the graphic.
What information can be obtained from time and frequency domain measures?
Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.
How is a function converted to a frequency domain?
A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a sum or integral of sine waves of different frequencies, each of which represents a frequency component.
How are sine waves used in data communication?
A single-frequency sine wave is not useful in data communication. We need to send a composite signal, a signal composed of many simple sine waves. According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes and phases.
How are waveforms described in the time domain?
1. Any waveform in the time domain can be completely and uniquely described by combinations of sine wave. 2. Any two sine waves with different frequencies are orthogonal to each other. If you multiply them together and integrate over all time, they integrate to zero.
How is a composite signal composed of sine waves?
We need to send a composite signal, a signal composed of many simple sine waves. According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes and phases. A composite periodic signal Decomposition of a composite periodic signal in the time and frequency domain