Consider the function: SketchX(omega). What is the Nyquist sampling frequency (H
ID: 1805973 • Letter: C
Question
Consider the function: SketchX(omega). What is the Nyquist sampling frequency (Hz)? Your boss asks you to modulate x(t). You decide to make a new function: . Sketch X1 (omega). After seeing your results, your boss is ecstatic! You don't quite see what the big deal is about your modulation, so your boss asks you to apply a lowpass filter, h(t), to x1(t) so that x2(t) = x1 (t) * h(t). What cutoff frequency do you choose? What is the Nyquist frequency of x2(t)? Your boss can't seem to make up her mind, and she asks you to recreate x(t) from x2 (0 by using the following equation: x(t) = x2(t)y(t) Find y(t).Explanation / Answer
The term Nyquist frequency has two related meanings, either as a measure of a digital system's performance or of an analog signal's requirements for a digital system. In the strictest sense it is a characteristic of processing systems that defines the maximum input frequency the system can resolve. Any frequency components in the input that are higher than this frequency result in an incorrect digital representation of the signal. A slightly different use of the term is as a characteristic of signals rather than systems. More properly called the Nyquist rate, this defines how frequently a digitizer must sample a specific analog signal to avoid this same distortion.