## Example 1.4

#### A square wave with a frequency of 1 MHz is mixed in a receiver with a local oscillator sinusoidal at 7.5 MHz and the resulting signal passed through a brick-wall low pass filter with a cut-off of 700 kHz.

1. What will appear at the output of the receiver?
2. The output of the receiver is found to be too small for practical use. How can this output level be increased simply by altering the shape of the 1 MHz modulating component?

### Solution

#### The square wave is made up of sinusoidal components given by the Fourier series as derived in Example 1.1. This signal, when mixed with the 7.5 MHz local oscillator, will give components at the sum and difference between each of the Fourier series components and the 7.5 MHz reference.
Only one of these components will fall within the bandwidth of the output low pass filter, hence the output waveform will be sinusoidal, with amplitude proportional to the amplitude of the seventh harmonic of the square wave.
In order to increase the output level from the filter, the amplitude of the seventh harmonic must be increased. This can be achieved by altering the mark space ratio of the square wave so that it becomes richer in harmonics (see Example 1.2).