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  • Low-side injection results in symmetry in the translated message spectrum about ± f c on each of the positive and negative half-axes.
  • High-side injection separates the undesired images further from the lower frequency portion (which will ultimatelybe retained to reconstruct the message). This eases the requirements on the bandpass filter.
  • Both high-side and low-side injection can place frequency interferers in undesirable places.This highlights the need for adequate out-of-band rejection by a bandpass filter before downconversion to IF.

Consider the system described in [link] . The message w ( t ) has a bandwidth of 22kHz and a magnitude spectrum as shown.The message is upconverted by a mixer with carrier frequency f c . The channel adds an interferer n . The received signal r is downconverted to the IF signal x ( t ) by a mixer with frequency f r .

  1. With n ( t ) = 0 , f r = 36 kHz, and f c = 83 kHz, indicate all frequency ranges (i)-(x) that include any partof the IF passband signal x ( t ) . (i) 0-20 kHz,(ii) 20-40 kHz, (iii) 40-60 kHz,(iv) 60-80 kHz, (v) 80-100 kHz,(vi) 100-120 kHz, (vii) 120-140 kHz,(viii) 140-160 kHz, (ix) 160-180 kHz,(x) 180-200 kHz
  2. With f r = 36 kHz and f c = 83 kHz, indicate all frequency ranges (i)-(x) that include anyfrequency that causes a narrowband interferer n to appear in the nonzero portions of the magnitude spectrum ofthe IF passband signal x ( t ) .
  3. With f r = 84 kHz and f c = 62 kHZ, indicate every range (i)-(x) that includes anyfrequency that causes a narrowband interferer n to appear in the nonzero portions of the magnitude spectrum ofthe IF passband signal x ( t ) .
Transmission system for Exercise 5-17
Transmission system for Exercise [link]

A transmitter operates as a standard AM with suppressed carrier transmitter (as in AM.m ). Create a demodulation routine that operates in two steps:by mixing with a cosine of frequency 3 f c / 4 and subsequently mixing with a cosine of frequency f c / 4 . Where must pass/reject filters be placed in orderto ensure reconstruction of the message? Let f c = 2000 .

Consider the schematic shown in [link] with the absolute bandwidth of the baseband signal x 1 of 4 kHz, f 1 = 28 kHz, f 2 = 20 kHz, and f 3 = 26 kHz.

  1. What is the absolute bandwidth of x 2 ( t ) ?
  2. What is the absolute bandwidth of x 3 ( t ) ?
  3. What is the absolute bandwidth of x 4 ( t ) ?
  4. What is the maximum frequency in x 2 ( t ) ?
  5. What is the maximum frequency in x 3 ( t ) ?
Transmission system for Exercise 5-19
Transmission system for [link]

Using your M atlab code from Exercise  [link] , investigate the effect of a sinusoidal interference:

  1. at frequency f c 6 ,
  2. at frequency f c 3 ,
  3. at frequency 3 f c .

Consider the PAM communication system in [link] . The input x 1 ( t ) has a triangular baseband magnitude spectrum. The frequency specifications are f 1 = 100 kHz, f 2 = 1720 kHz, f 3 = 1940 kHz, f 4 = 1580 kHz, f 5 = 1720 kHz, f 6 = 1880 kHz, and f 7 = 1300 kHz.

  1. Draw the magnitude spectrum | X 5 ( f ) | between ± 3000 kHz. Be certain to give specific values of frequency andmagnitude at all breakpoints and local maxima.
  2. Specify values of f 8 and f 9 for which the system can recover the original message without corruption with M = 2 .
Transmission system for Exercise 5-21
Transmission system for Exercise [link]

This problem asks you to build a receiver from a limited number of components.The parts available are:

  1. two product modulators with input u and output y related by
    y ( t ) = u ( t ) cos ( 2 π f c t )
    and carrier frequencies f c of 12 MHz and 50 MHz
  2. two linear bandpass filters with ideal rectangular magnitude spectrum of gain one between - f U and - f L and between f L and f U and zero elsewhere with ( f L , f U ) of (12MHz, 32MHz) and (35MHz, 50MHz).
  3. two impulse samplers with input u and output y related by
    y ( t ) = k = - u ( t ) δ ( t - k T s )
    with sample periods of 1/15 and 1/12 microseconds
  4. one square law device with input u and output y related by
    y ( t ) = u 2 ( t )
  5. three summers with inputs u 1 and u 2 and output y related by
    y ( t ) = u 1 ( t ) + u 2 ( t ) .

The spectrum of the received signal is illustrated in [link] . The desired baseband output of the receivershould be a scaled version of the triangular portion centered at zero frequency with no other signalsin the range between - 8 and 8 MHz. Using no more than four parts from the 10 available,build a receiver that produces the desired baseband signal. Draw its block diagram.Sketch the magnitude spectrum of the output of each part in the receiver.

Spectrum of the received signal for Exercise 5-22
Spectrum of the received signal for Exercise [link]

For further reading

A friendly and readable introduction to analog transmission systems can be found in

  • P. J. Nahin, On the Science of Radio , AIP Press, 1996.

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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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