Articles | Page 33 of 35

A BPSK constellation in a the presence of a carrier phase offset. A hypothetical QPSK constellation is also shown for comparison

July 23, 2016 Wireless/SDR

How to Detect a Carrier Lock in an SDR

We have discussed before the effect of a phase offset on the received signal. We have also seen a logical approach to solve this problem as well as one of the earliest algorithms for phase synchronization known as a Costas loop. Here, the purpose is to explain how a Rx detects whether the Phase Locked Loop (PLL) has acquired the lock. A receiver is simply a blind machine which can implement a PLL but can never get to know how it is actually doing. A lock detector is a logic signal used in the Rx to indicate successful synchronization after

July 21, 2016 DSP

Some DFT Properties

The purpose of this article is to summarize some useful DFT properties in a table. My favorite property is the beautiful symmetry depicted by continuous and discrete Fourier transforms. However, if you feel that this particular content is not as descriptive as the other posts on this website are, you are right. As opposed to the rest of the content on the website, we do not intend to derive all the properties here. Instead, based on what we have learned, some important properties of the DFT are summarized in the table below with an expectation that the reader can derive

July 20, 2016 DSP

Time-Invariant Systems

A system is time-invariant if shifting the input sequence on time axis leads to an equivalent shift of the output sequence along the time axis, with no other changes.

The blue line is the signal template and while red is the matched filter. Notice the same magnitude on each spectral line but exactly opposite phase

July 18, 2016 DSP / Wireless/SDR

Demodulation – From Signals Back to Numbers

Remember that in the article on correlation, we discussed that correlation of a signal with proper normalization is maximum with itself and lesser for all other signals. Since the number of possible signals is limited in a digital communication system, we can use the correlation between incoming signal $r(nT_S)$ and possible choices $s_0(nT_S)$ and $s_1(nT_S)$ in a digital receiver. Consequently, a decision can be made in favor of the one with higher correlation. It turns out that the theory of maximum likelihood detection formalizes this conclusion that it is the optimum receiver in terms of minimizing the probability of error.

July 17, 2016 DSP

Sampling a Continuous-Time Signal

Most signals of our interest — wireless communication waveforms — are continuous-time as they have to travel through a real wireless channel. To process such a signal using digital signal processing techniques, the signal must be converted into a sequence of numbers. This can be done through the process of periodic sampling. From Continuous to Discrete Time Consider a band-limited continuous-time signal $s(t)$ and its frequency domain representation $S(F)$ with bandwidth $B$, shown in the above figure. A discrete-time signal $s[n]$ can be obtained by taking samples of $s(t)$ at equal intervals of $T_S$ seconds. This process is shown in