9

You can also think of delta encoding as linear predictive coding (LPC) where only the prediction residual ($x[n]-\hat{x}[n]$ in @robertbristow-johnson's notation) is stored and the predictor of the current sample is the previous sample. This is a fixed linear predictor (not with arbitrary coefficients optimized to data) that can exactly predict constant ...


6

That's used a lot. See for example https://en.wikipedia.org/wiki/Delta_encoding, https://en.wikipedia.org/wiki/Run-length_encoding. "Looking Smooth" typically means "not a lot of high frequency content". The easiest way to take advantage of this, is to figure out what the highest frequency really need then low-pass filter and choose an lower sample rate. ...


6

Another notion you might wanna look into for lossless compression of a bandlimited signal (it's this bandlimiting that gets you this "smoother ... signal, ...closer ... to the baseline") is Linear Predictive Coding. I think this is historically correct that LPC was first used as a variant of Delta coding where the LPC algorithm predicts $\hat{x}[n]$ from ...


5

You think the Shannon-Hartley Theorem is in conflict with Full Duplex (in the sense you describe), and luckily it's not! The problem really is that your $\eqref{SNR}$ formula isn't relevant for the Shannon-Hartley Theorem (SHT). With respect to the SHT, your $t_A$ isn't noise! That's easy to explain. SHT makes a statement about the channel capacity $C$, i....


5

Three reasons to increasing the sampling rate further are 1) To relax the requirements of the post D/A conversion filtering for image rejection. 2) Increase signal SNR by spreading quantization noise for a fixed number of DAC bits across a wider frequency range. 3) Minimize passband droop in the D/A reconstruction. Reason 1 is the most dominant one in my ...


4

A square operation creates an unmodulated tone for a BPSK signal at 2x the carrier frequency (a pure tone for the case that the signal was unfiltered or rectangular pulses with perfect phase and amplitude balance in the BPSK modulation, and typically a stronger carrier with weaker sidebands in the more common filtered or pulse-shaped cases). For QPSK signals ...


4

Whenever you are dealing with real signals, be it in baseband or passband, the magnitude spectrum is symmetrical around $f=0$. For mathematical convenience, quadrature signals are often written as complex. A baseband quadrature signal (also called the "complex envelope" or the "low-pass equivalent signal") is complex, and its magnitude spectrum is no longer ...


4

Yes, of course, you can sum them. The bandwidth of the resulting signal is simply the min/max of the individual signals. If we assume $$z(t)=x(t)+y(t)$$ Then then bandwidth of $z(t)$ will simply be $[min(f_{min},g_{min}),max(f_{max},g_{max})]$, so in general the you will have $B_z > B_x$ Keep in mind that for any real valued signal $x(t)$ the spectrum ...


4

The Gardner Timing Error Detector is diagrammed in the graphic below, where two samples per symbol are used, and the error is determined using Prompt*(Late-Early), and when synchronized the center sample (Prompt) will be midway between two symbols. In contrast, an Early-Late approach uses (Late-Early), typically on a correlated symbol response, and when ...


4

Consider a band-limited function $u(t)$ sampled at an appropriate sampling rate $f_s=1/T$ such that it is perfectly represented by its samples $u(kT)$. If those samples are quantized resulting in values $v(kT)$ then it can be shown that the mean-squared error $$\epsilon=\sum_k\big|u(kT)-v(kT)\big|^2$$ is equal to the mean-squared error between the ...


3

Ordinary Least Squares problem Your $$\hat x = \arg\min_x \sum_{n=1}^{N_r} \left\lvert y_n - h_n x\right\rvert^2$$ is just a way of saying $$\hat x = \arg\min_x \left\| y - Hx \right \|$$ and that is called an Ordinary Least Squares estimation problem. Its objective function is of a quadratic form, so we don't have to actually iteratively optimize or ...


3

Actually, magnetic induction is a current research topic for underwater communications, see http://bwn.ece.gatech.edu/papers/2015/j14.pdf. Also, this paper includes a nice comparison of underwater communication strategies, including electromagnetic waves, acoustical communication, and optical communication. One major disadvantage of magnetic induction is ...


3

The short answer is: if you transmit one block of $N$ symbols (no data before it for at least $L$ symbol times) over a frequency-selective channel of length $L$, then the channel matrix will be of dimension $NN_TN_R\times N$. The long answer: start with $N_T=N_R=1$. Then the $n^{\text{th}}$ received sample can be written as $$y_n=\sum_{l=0}^Lh_lx_{n-l}+...


3

This simply reflects the load asymmetry of real world applications. On most networks, traffic is dominated by content streaming, which is a download activity. Netflix alone accounts for 15% of the world's entire Internet traffic.


3

In brief, we consider the channel as frequency-selective channel if the frequency of the signal is larger than then frequency of channel No offense, but that ought to win the prize for the least-accurate definition of frequency-selectivity I heard ;-) What you mean is channel is frequency-selective if the bandwidth of the signal is larger than the ...


3

The receiver/transmitter pair in B's possession is operating in half-duplex mode. As you say "$A$ give $x$ to $B$, then $B$ give $x$ to $C$" which specifies that while $B$ ls listening to what $A$ is telling it (the $x$ that is being given to $B$), the transmitter in $B$'s possession must remain silent until $B$ has completely received $x$. It is only ...


3

QAM is a digital modulation scheme. As such it is one way of implementing a physical layer that allows to convey digital information over a given medium. QAM is frequently used in all kinds of systems, including wireless (cf. broadcast TV and yes, also WiFi) as well as wired (Ethernet uses some variations of QAM as well). What kind of information you convey ...


3

Quantization and encoding are largely independent. "Symbols" is another word for "pulses", and the line encoding can also play a role in how the information is transmitted. Say you quantize one sample to $256 = 2^8$ levels, or 8 bits/sample. In order to transmit those 8 bits, you can, among other options: use binary encoding, which requires transmitting ...


3

Eventhough Laurent has given a broader sense of the answer, let me put here the communications theory sense ot it. The concept of instantaneous freqency emerges when you consider Frequency Modulation or Phase Modulation systems, where the message is embedded into the change of the frequency or phase of a carrier signal. This carrier is typically a single ...


3

My first inclination is to say this is a meaningless question. The concept of "instantaneous" frequency really only pertains to a single pure tone with a slightly varying frequency. In this light, one may construct a definition saying "The instantaneous frequency at time $t$ is the same as that of a pure tone which matches the function (sum) in the ...


2

Assuming one antenna transmits one symbol per time unit, then 16 symbols require 4 time units to be out. Then it is simply that r_1 = H_1 * x_1(1:4) r_2 = H_2 * x_1(5:8) r_3 = H_3 * x_1(9:12) r_4 = H_4 * x_1(13:16) If channel H is fixed during these 4 time units, [r_1 r_2 r_3 r_4] = H * [x_1(1:4) x_1(5:8) x_1(9:12) x_1(13:16)]; or r = reshape(H*reshape(...


2

Since the bandwidth stays constant at 120 kHz, the symbol rate needs to be reduced: $$R_s = W_m/(1+\alpha) = 120000/2 = 60000 \text{ symbols per second.}$$ Then the bit rate is $R_b = 6R_s=360,000 \text{ bits per second.}$ The transmission duration is then $$T = \frac{48 \times 10^6 \text{ b}}{360 \times 10^3 \text{ b/s}} = 133.3 \text {s}.$$


2

The training sequence should be at the same spacing as the equalizer when considering its sampling at the input to the equalizer. Adaptive algorithms converge to the least square solution based on the error between the received sequence and the transmitted sequence (known when a training sequence is used). Further, the equalizer can only determine a solution ...


2

The OP stated he was interested in $\pi/4$-DQPSK (not QPSK), so phase synchronization is presumably not an issue for him. As far as the actual implementation is concerned, you'll save yourself some time if you become familiar with the bottom of pages 29 (symbol mapping) and 37 (differential detection) in this student paper. Ignore all the old TI DSP-chip ...


2

If you have two sinusoidal length $N$ sequences $$x_1[n]=\sin\left(n\omega_1+\phi_1\right),\qquad n\in[0,N-1]\\ x_2[n]=\sin\left(n\omega_2+\phi_2\right),\qquad n\in[0,N-1]\tag{1}$$ then for orthogonality we require $$\sum_{n=0}^{N-1}x_1[n]x_2[n]=0\tag{2}$$ For the given sequences $(1)$ we obtain $$\begin{align}\sum_{n=0}^{N-1}x_1[n]x_2[n]=&\sum_{n=...


2

The disadvantage is that the signal V21 = V1 + V2 = [2, 0, 2, 0] disappears every other chip interval which makes maintaining carrier and phase synchronization more difficult. Also, while the total energy in V21 is equals to the sum of the energies of V1 and V2, V21 uses 4 times the instantaneous power needed by either V1 or V2 and so the transmitter needs ...


2

Rate: the actual rate you transmit data at. Throughput: the percentage of signal data that is actually delivered correctly to the receiver in the overall data (signal data + coding + overhead ... etc). Capacity: maximum rate that a channel allows for a given SNR such that the received signals can be reliably decoded at the receiver.


2

As best as I can tell from the terminology, QPSK a.k.a. 4-PSK or 4-QAM can convey twice the number of bits of information as BPSK in the same bandwidth. Given a one-sided bandwidth of $B$ and assuming sufficient S/N ratio so that no bits are corrupted, BPSK can transfer bits at a rate of $2B$. That means, given the same one-sided bandwidth, QPSK can ...


2

Well, you're not going to send and receive those symbols directly, you know? What you'll need to convey the information over a channel is a waveform. Your receiver will then typically use the same waveform to correlate the signal. Say you are using root raised cosine pulses to transmit, then your receiver will employ a root raised cosine filter as a pulse ...


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