Question

Input Signal

a.​​​​​​​Create the signal x(t), which is specified in Eq. (1) and has the frequencies f1=20 Hz, f2=50 Hz, f3=1 kHz, and f4=5 kHz. The signal has a 0.5 second duration, and the sampling frequency is 20 kHz.

x(t) = 5sin(2πf1t) +cos(2πf2t) + 15cos(2πf3t) + 10cos(2πf4t) (1)

Answer 1

To create the signal x(t) with specified frequencies, one would use digital signal processing software or coding to sample and generate the signal utilizing the given formula over a 0.5-second duration at a 20 kHz sampling frequency.

Step-by-step explanation:

To create the signal x(t), with frequencies f1=20 Hz, f2=50 Hz, f3=1 kHz, and f4=5 kHz, you follow a specific set of steps. Given the content loaded Input Signal equation x(t) = 5sin(2πf1t) + cos(2πf2t) + 15cos(2πf3t) + 10cos(2πf4t), you can generate this signal using a digital signal processing software or a programming tool that is capable of handling the discrete-time signals.

To sample this signal at a sampling frequency of 20 kHz for a 0.5-second duration:

Calculate the time vector with a timestep of 1/20000 seconds, covering the duration of 0.5 seconds.

Calculate the signal values for each time step using the provided equation.

Store and, if necessary, plot these values to visualize the signal waveform.

The resulting signal will comprise superposed sinusoidal waves with the specified amplitudes and frequencies, showcasing both low and high-frequency components.