Homework Assignment #4

EE475���������������� Fall 2003

Assigned:� Thursday, October 30, 2003

Due AT THE START OF CLASS on Thursday, November 13, 2003

A simple signal generator can be constructed by sending a periodic sequence of digital values to a digital-to-analog converter.� The periodic sequence can either be calculated �on the fly� or a stored data table can be used.

If you want to generate a periodic signal with frequency f, the mathematical expression is

where A is the desired output amplitude and f_s is the sampling rate of the digital-to-analog converter (DAC).� If you are able to use floating point math, the expression above can be implemented directly in software.� However, it may happen that floating point math is too slow, or it may require too much program memory if the processor does not have floating point hardware.� In this case it may be possible to pre-calculate one cycle of the desired sinusoid in advance and store it in a static memory array.� You will use both techniques in this homework assignment.� Rather than writing to a real DAC, you will write the results into a file as a sequence of integer (text) values.

Problem #1:� Write a C program that generates several cycles of a sinusoidal waveform using the floating point formula above, and write the result as a text file.� The output needs to be 16-bit 2�s complement integer numbers in text form, so round the floating point number to the nearest integer before writing to the file.� Use A=32767, and f_s = 5 kHz in your code.� The command line for your program should be something like:

sine_gen� f� cycles� out_file

where sine_gen is the name of your program, f is the desired sinusoid frequency in Hz, cycles is the integer number of waveform cycles to produce, and out_file is the name of the output text file to be created.

Try several different frequencies and observe several output cycles:� comment on the periodicity of the output data.� What happens if the frequency f is not an integer factor of 5 kHz?

Problem #2:� Now modify your C program or create a new program that uses a sinusoidal lookup table (as discussed in class) to generate the output sequence instead of calculating the sin() function on the fly.� You must use the include file �sinetable.h� from the course web site to define the lookup table data.

Use the same command line format as for Problem #1.

You can use floating point math to compute the sample increment and lookup index, but the output must come from the lookup table.� You can use either a �round to nearest� lookup strategy or linear interpolation.