Digital Signals
What makes a digital signal "digital"?
It takes on discrete values. These values are representative of the true values in that they may not EXACTLY represent the true value.
Describe the unit impulse.
It is an instantaneous burst. We can think of it as a clap, though in reality we see that a true instantaneous signal such as an impulse is nonexistent. We model it in the world of engineering as an arrow.
What unit is the x-axis for a signal's spectral plot?
Frequency
What data types are 5, 5.1, and 'five'?
They are an integer, float, and string.
Provide a fun fact you learned from a Tech Highlight session this week.
[Multiple answers acceptable.]
Name two reasons we like to use digital signals in modern technology.
1) It is compatible with computers and easily transferable.
2) It is inherently more noise resistant.
3) Ages better than analog devices.
When would we use a unit step function?
Unit steps are often used to describe the turning on/off of something.
What is the minimum and maximum values in frequency that a signal's spectra can have in terms of its sampling frequency?
-fs/2 and fs/2 where fs is the sampling frequency.
Name one difference between a list and a tuple.
A list is made using square brackets [ ] and is changeable.
A tuple is made using round brackets ( ) and is unchangeable.
What frequencies can the human ear hear?
From about 20 Hz to 20,000 Hz. This is why a popular sampling frequency is 44.1 kHz.
How do you calculate the Nyquist sampling frequency?
The Nyquist sampling frequency must be twice the highest frequency.
fs=2fmax
If you have a signal y(t) = x3, how would you modify it to move it left by 1 in x?
ymoved left 1(t) = (x+1)3
What does a tone look like in the frequency domain?
An impulse at its frequency.
Provide a scenario in which a for-loop could be useful.
[Multiple answers acceptable.]
Perhaps, cycling through a grocery list as shown in our Jupyter notebook examples.
What frequencies are WiFi at?
2.4 and 5 GHz
If we have a 6-bit ADC that reads a max voltage of 10V and min voltage of -10V, what is the resolution of the signal?
The range of voltage is naturally 20V. Since resolution is the range divided by the number of levels, we get that...
resolution = 20/(26-1) = 0.3175V
In the equation y(t) = 4sin(2π110t+10) volts, what is the amplitude, frequency, and phase shift? Provide units.
The amplitude is 4 volts. The frequency is 110 Hz. The phase shift is -10 radians or 573 degrees.
You could also describe the phase shift in terms of time...
-10 [rad] / (110 [1/sec] * 2π [rad]) = -0.0145 [sec]
How do we like to visualize time-varying signals in the frequency domain?
We like to use a function called the STFT or spectrogram. It uses a sliding window to take the FFT of a signal over time and plot the magnitudes using color so that the x-axis can be time and the y-axis can be frequency.
How do you make a function? Provide some syntax.
def function_name (input1, input2,...):
#code
return output1, output2, ....
How did ultrasound transducers look at a single point?
The delay the sound from each little electrode of the array in the transducer such that they all will hit a particular point.
If we sample at 500 Hz a signal that is 400 Hz, what frequency will it appear at in the signal spectra?
Recall that fapparent=|f-(fs/2)(k+1)|...
so fapparent=|400-(500/2)(1+1)|=100 Hz.
If y1(t) = u(t) and y2(t) = -2u(t) = -2y1(t), describe the changes done on y2(t) when compared to y1(t). (Recall that u(t) is the unit step function.)
1. The unit step is flipped across the t-axis.
2. The unit step is stretched in y by 2.
Concisely describe how the Fourier transform separates out frequencies from any given signal.
You can think of it as wrapping the signal around a circle and varying the wind frequency. The center of mass of this wrapped wire pattern then gives us the height of our Fourier transform at each wrap frequency.
We've been using Matlibplot to plot multiple signals. What does the following line of code mean?
plt.subplot(121)
It means that we are using Matlibplot via a shorthand as plt. Specifically, we are using a function contained in this library to create subplots, or multiple plots in one display. The first 1 refers to the number of rows of subplots. The 2 refers the number of columns of subplots. Then, the last 1 refers to the fact that we are currently calling out the first of these two subplots.
What two signals did Mobashir say helped researchers at Duke identify possible COVID cases so that they could better allocate limited COVID tests to a population?
Average heart rate and steps from a smart watch