Signal Processing for Communication Systems
Raised-cosine (RC) pulse shaping filter is generally employed at the transmitter. In time domain, a matched filter at the receiver is the mirrored copy of the impulse response of the transmit pulse shaping filter.
In square-root raised cosine (SRRC) filtering, the task of raised cosine filtering is equally split between the transmit and receive filters. The combined impulse response of two SRRC filters is same as the impulse response of the RC filter
As mentioned earlier, the shortcomings of the sinc pulse can be addressed by making the transition band in the frequency domain less abrupt. The raised-cosine (RC) pulse comes with an adjustable transition band roll-off parameter , using which the transition band’s rate of decay can be controlled. The RC pulse shaping function is expressed in … Read more
Key focus: Sinc pulse shaping of transmitted bits, offers minimum bandwidth and avoids intersymbol interference. Discuss its practical considerations & simulation. Sinc pulse shaping As suggested in the earlier post, the pulse shape that avoids ISI with the least amount of bandwidth is a sinc pulse of bandwidth . Here, is the baud rate of … Read more
Key focus: Rectangular pulse shaping with abrupt transitions eliminates intersymbol interference, but it has infinitely extending frequency response. Simulation discussed. Rectangular pulse A rectangular pulse with abrupt transitions is a natural choice for eliminating ISI. If an information sequence is shaped as rectangular pulses, at the symbol sampling instants, the interference due to other symbols … Read more
Key focus: Baseband communication system and its equivalent DSP implementation (discrete time model) with a pulse shaping & matched filter is briefly introduced. If a train of pulses representing an information sequence need to be sent across a band-limited dispersive channel, the bandwidth of the channel should be large enough to accommodate the entire spectrum … Read more
Key focus: As per Nyquist ISI criterion, to achieve zero intersymbol interference (ISI), samples must have only one non-zero value at each sampling instant. Consider an equivalent baseband communication system model with baud rate ( is the symbol period) shown in Figure 1, where the transmitter, channel and the receiver are represented as band-limited filters. … Read more
Key focus: Inter-symbol interference: symbols sent through a dispersive channel, arrive at different time intervals and interfere due to non-constant group delay. Introduction Communication systems have progressed from analog to digital implementation due to the latter’s advantages of bandwidth efficiency and exceptional immunity to noise. The greatest challenge to a communication systems engineer lies in … Read more
In coherent detection, the receiver derives its demodulation frequency and phase references using a carrier synchronization loop. Such synchronization circuits may introduce phase ambiguity in the detected phase, which could lead to erroneous decisions in the demodulated bits. For example, Costas loop exhibits phase ambiguity of integral multiples of radians at the lock-in points. As … Read more
Key focus: Demodulation of phase modulated signal by extracting instantaneous phase can be done using Hilbert transform. Hands-on demo in Python & Matlab. Phase modulated signal: The concept of instantaneous amplitude/phase/frequency are fundamental to information communication and appears in many signal processing application. We know that a monochromatic signal of form x(t) = a cos(ω … Read more
Key focus: Learn how to use Hilbert transform to extract envelope, instantaneous phase and frequency from a modulated signal. Hands-on demo using Python & Matlab. If you would like to brush-up the basics on analytic signal and how it related to Hilbert transform, you may visit article: Understanding Analytic Signal and Hilbert Transform Introduction The … Read more