Digital Signal Processing : disign Stereo Demultiplexing

Stereo multiplexing is a form of frequency division multiplexing used in FM radio to transmit two separate audio signals ml(t) and mr(t) at the same time. Designed to be compatible with monophonic receivers, FM radio stereo multiplexing generates a sum signal, [ml(t) + mr(t)], and a difference signal, [ml(t) − mr(t)]. A reference tone cos(2 π fct) at frequency fc is included for coherent detection and a frequency-doubled subcarrier cos(4 π fct) modulates the difference signal into a double sideband suppressed carrier (DSBSC) wave. The resulting composite wave is: m(t) = [ml(t) + mr(t)] + [ml(t) − mr(t)]cos(4 π fct) + cos(2 π fct). Therefore, a stereo demultiplexer is required at the FM receiver to recover the two audio signals. Your task is to design and implement in MATLAB a stereo demultiplexer using properly designed digital filters to separate the two audio signals from the composite signal recorded in the WAVE file [login to view URL] composite signal recorded in your WAVE file is generated using stereo multiplexing as detailed above, at a sampling frequency of 44.1 kHz. It contains two 10-second segments picked randomly from the first and second halves of a well-known song. To limit the bandwidth of these audio segments, both signals have been processed by a lowpass filter with a stopband edge frequency of 6 kHz. The reference frequency fc was randomly selected from the range of 7-9 kHz at the time of generation. The composite signal can be loaded into MATLAB by using the wavread command. The DSBSC wave has its spectrum centred at 2fc. The following equation shows the process of coherent detection. [ml(t) − mr(t)]cos(4 π fct) × cos(4 π fct) = [ml(t) − mr(t)] × ½[1 + cos(8 π fct)] = ½[ml(t) − mr(t)] + ½[ml(t) − mr(t)]cos(8 π fct) where the difference signal ½[ml(t) − mr(t)] can be obtained by lowpass filtering. The derivation above uses the following trigonometric identity: cos2 α = ½[1+cos(2 α )]. Include a block diagram of your stereo demultiplexer and explain your design justifying the choices of digital filters.