For the deterministic signal y(t) 2 + 3 sin(int) + 4 sin(18), sketch the amplitu
ID: 2248227 • Letter: F
Question
For the deterministic signal y(t) 2 + 3 sin(int) + 4 sin(18), sketch the amplitude-frequency spectrum of y(t) (a) when the signal is sampled at a rate of 24 Hz (indicate by solid lines) and (b) when it is sampled at a rate of 12 Hz (indicate by dashed lines). Finally, (c) determine the minimum sample period (in s) to avoid amplitude ambiguity in the amplitude-frequency spectrum. Final Answers: (Please provide additional explianation): (a) f, 24 Hz. So fa 24/2 = 12 Hz, which is greater than the highest frequency of 9 Hz in the signal. Thus there is no aliasing. The spectrum has three lines', one of amplitude 2 at 0 Hz, one of amplitude 3 at 3 Hz, and one of amplitude 4 at 9 Hz, shown as solid lines in Figure 10.2 (b) = 12 Hz. So fN = 12/2 = 6 Hz, which is less than the highest frequency whose component will be aliased k = f/fx4-9/6-1.5. So, ka-0.5 and fa-kafN-0.5x 6-3 Hz. Thus, there will be two components at 3 Hz. Their amplitudes combine in quadra- ture. The 'line' at 3 Hz w have an amplitude of 32425. There are now two lines', each shown in Figure 10.2 as dashed lines. (c) The minimum sample time will be the least common multiple of the compo- nents' periods, which are 1/3 s and 1/9 s. Thus, the minimum sample time is 1/3 S.Explanation / Answer
a)In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.For functions which varyingwith time, let s(t) is a continuous function (or "signal") which is to be sampled, and let the sampling be performed by measuring the value of the continuous function every T seconds, which is called the sampling interval or the sampling period.
b)since given fs=24hz for a rate of 12 hz which is given by fn=24/2=12Hz whose component will be aliased.
Aliasing is an effect that causes different signals to become indistinguishable from each other during sampling. Aliasing is characterized by the altering of output compared to the original signal because resampling or interpolation resulted in a lower resolution in images, a slower frame rate in terms of video or a lower wave resolution in audio. Anti-aliasing filters can be used to correct this problem.
c)The sampling frequency or sampling rate, fs, is the average number of samples obtained in one second (samples per second), thus fs = 1/T.
• Aliased (false) frequencies can be determined using a foldingdiagram.
• Amplitude ambiguity can be avoided by setting the sample period equal to the least common multiple of all of the signal’s contributory periods.