How to create analogue signal?

Electrical Engineering - DSP analogue signal question?

• could someone please help me with the following question On the NanoBoard the anti-aliasing and reconstruction filters are passive low pass filters both with nominal cut-off frequencies around 10 kHz. The Maxim MAX1104 is a full codec and so contains both analogue to digital (A2D) and digital to analogue (D2A) converters, these being represented by the sample and hold (S/H) plus quantiser (Q) and D/A blocks in Figure 1 respectively. Finally, the DSP block in Figure 1 is where the difference equation for implementing the desired digital filter is performed. figure 1 is a block diagram of the following x(t)->anti-aliasing filter->S/H->Q->DSP->D/A->reconstruction filter->y(t) Could someone help me with these questions questions: 1. Bearing in mind that the anti-aliasing filter on the NB1 is not ideal, explain what happens to the analogue signal, x(t), after it has passed through this filter and is presented to the input of the A2D, when: a. x(t) is a sinusoidal signal of frequency 10 kHz. b. x(t) is a square wave (50% duty cycle) of fundamental frequency 4 kHz. Hint, think about what the Fourier series representation of this square wave signal is. Any help would be appreciated, Thanks.

• Answer:

  a. Since the cutoff frequency of the filter is 10 kHz and the signal is 10 kHz, that means that only 1/2 the power (0.7071 of the voltage) of the 10 kHz source signal will be present at the input of the A2D. In other words, there will still be a significant voltage present at the A2D. b. With a square wave, you have harmonics -- mostly odd harmonics -- present in the wave, so you will have 4 kHz, 12 kHz, 20 kHz, 28 kHz, 36 kHz, etc... out to infinity. If you do a Fourier seried on the square wave, the levels of these harmonics are: (1st) 4 kHz : 1 (3rd) 12 kHz : 0.634 (5th) 20 kHz : 0 (7th) 28 kHz : 0.210 (9th) 36 kHz : 0 (11th) 44 kHz : 0.127 etc. The 10 kHz filter will have to filter out the components of the signal higher than 10 kHz -- that is, all the harmonics of the square wave. The filtered levels of the 3rd, 7th, 11th etc. harmonics will be reduced even further than the original levels indicated above. .