Aliasing
Speedy-33 instructions:
We will now look at aliasing and its effect on the sampled signal. As you know, aliasing exists whenever signalfrequencies greater than Fs/2 are sampled using a sampling frequency of Fs. To eliminate aliasing, most sound cards and DSPboards have some sort of built-in analog anti-aliasing filter that removes all input signals greater than a certain frequency prior tosampling. It is important to remember that anti-aliasing filters must do the filtering prior to sampling–otherwise, the high-frequency signals would have already aliased to lowerfrequencies by the sampling process.
Some boards (and most Soundcards) have anti-aliasing filters with variable cutoff frequencies that removeall frequencies>Fs/2. As Fs changes, the cutoff frequency of the anti-aliasing filter changes as well. If a boardhas a variable frequency anti-aliasing filter that is always set to Fs/2, there will never be aliasing (at least in theory). Althoughthis type of operation is ideal from a performance point of view, it doesn’t allow the user to examine the effect of aliasing. The SPEEDY-33 does not have an anti-aliasing filter. Any frequencygreater than 24kHz can cause aliasing if the sampling frequency is set to 48kHz.
- Set the sampling frequency to 48000 Hz (in both the Analog Input and Analog Output nodes).
- Set the function generator to a 0.2 V, 100 Hz, sinusoid.
- Move thearrows on the function generator so that the hundreds-digit on the frequency display is flashing.
- You can now easily increase the frequency in steps of 100 Hz. by pressing thebuttons.
- Run the program and observe the frequency display, time display, and sound as you sweep the signal frequencyfrom 100 Hz. to 50 kHz.
- Pay particular attention to the amplitude and sound of the reconstructed signal for input frequencies>24 kHz.
Answer these questions
Describe what you hear and see (especially the frequency spectrum) when you sweep the sinusoid frequency from 100 Hz. to 50 kHz. Take special note of what happens to both the amplitude and frequency of the reconstructed sinusoid once you get past 24 kHz.
- Repeat the experiment above, but set the sampling frequency to Fs = 8000 Hz. Here, pay special attention to what happens onceyou get above 4 kHz.
Answer these questions
What happens to the amplitude of the reconstructed signal once the input signal frequency hits 24 kHz? Explain.