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Unformatted text preview: L4 Fourier transform and AM radio In Lab 4, you will finally connect all of your receiver components and tune an AM radio broadcast. You will follow the radio signal through the entire system, from antenna to loudspeaker, in the time domain and the frequency domain. 1 Prelab The Fourier transform is an important tool in the analysis of your AM radio receiver. Make sure you understand the theory before you come to lab. 1. Find the Fourier transforms of rect and sinc signals shown in Figures L4.1a and b. By definition, F ( ) , the Fourier transform of signal f ( t ) is F ( ) = - f ( t )e- j t dt . Do not just use the look-up tables for the first transform. a) b) (a) ! 5 5 x 10 ! 4 t f(t) 2.5 ! 2.5 1 (b) t f(t) t = pi/6 1 Figure L4.1: rect and sinc functions for prelab. 341 L4 Fourier transform and AM radio 2. Read part 2.3 of the lab instructions, AM Radio Receiver, on pages 344-347. This will save you time in lab. 2 Laboratory exercise Equipment: Function generator, oscilloscope, protoboard, and wires. Components: Three-stage circuit from Lab 2, band-pass filter from Lab 3, RF amplifier, and mixer. 2.1 Fourier Transform It can be di ffi cult to identify features in the oscilloscopes display of the Fourier transform if you do not know what to expect. In this section, you will learn to identify features in the Fourier transform by looking at the Fourier transforms of some well known signals. 1. No circuit is used for this part of the laboratory. Connect the function generators output to Channel 1 of the oscilloscope. 2. Set the function generator to create a 1 kHz square wave with amplitude 1 V peak-to-peak. Turn on burst mode by pressing Shift then Burst. 3. Set the oscilloscope to display the magnitude of the Fourier transform of a segment of the input signal: Press +/- Turn on Function 2 Press Menu Press Operation until FFT appears Set the Operand to Channel 1 Set the time/div to 2 ms (you may need to adjust this later) Press FFT Menu Set the window to Hanning 1 Set the units/div to 10 dB and the ref level to 0 dBV Set the center frequency to 12.2 kHz, and set the frequency span to 24.4 kHz. To choose the center frequency and frequency span, press the appropriate button and use the cursor knob to change the frequency. If the oscilloscope tells you that the center frequency or frequency span is at a limit, increase or decrease the time/div and try again. 1 As a result of this choice, the incoming signal f ( t ) is e ff ectively multiplied with w H ( t ) rect ( t T ) cos 2 ( t T ) prior to Fourier transformation. This procedure limits the length of the Fourier transform segment to duration T of the window function w H ( t ) . Alternative window functions such as w B ( t ) = rect ( t T ) give rise to frequency spectra | F ( ) | with slightly di ff erent resolution and sidelobe details....
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- Spring '08