46 votes
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Why can so little digital information be stored on a cassette tape?

I had heard that tape is still the best medium for storing large amounts of data. well, "best" is always a reduction to a single set of optimization parameters (e.g. cost per bit, ...
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22 votes
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Can we break the Shannon capacity?

Most certainly not. While there has been some claims to break Shannon here and there, it usually turned out that the Shannon theorem was just applied in the wrong way. I've yet to see any such claim ...
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16 votes

Can we break the Shannon capacity?

The capacity of a channel should be viewed as analogous to the speed limit on a highway. It is possible to travel at a speed greater than the posted limit on a highway but it is not possible to ...
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12 votes

Deriving SER & BER for 4QAM, 16QAM and 32QAM

I will try to give a relatively simple answer to a complex question. I will not give any exact expressions for the error rates for two reasons. The first I stated in my initial sentence, the second is ...
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11 votes
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Why do we integrate the modulating function in FM?

You need to integrate the modulating signal because frequency is the time derivative of phase. Therefore, the typical relationship from introductory calculus holds: $$ \phi_i(t) = \int_{-\infty}^{t} \...
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10 votes
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FSK Demodulation, Bit Timing Recovery

I am currently implementing acoustic FSK modulation and demodulation. I am not a signal processing guy… Since you say you have matched filters, and you mention non-coherent detection, I think you're ...
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10 votes
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why is the z transform transfer function 1/(z-1) called an integrator?

There are a couple reasons. One is that $(1-z^{-1})$ represents $x[n]-x[n-1]$ which is a finite difference over a very small period of time. and that is an approximation to a differentiator. The ...
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9 votes
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What is a $BT$ (Bandwidth-Time) product with reference to modulation?

The $BT$ product is the bandwidth-symbol time product where $B$ is the $-3\textrm{ dB}$(half-power) bandwidth of the pulse/filter and $T$ is the symbol duration. For different applications you will ...
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9 votes
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Numerically Controlled Oscillator (NCO) for phasor implementation?

The NCO is a cyclical counter that can go on indefinitely but is otherwise similar to what you suggest in that you are increment n to set the output rate. It basically is a look up table of all the ...
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9 votes

Envelope behavior dIfference between QPSK, OQPSK and $\pi/4$-QPSK

Let's look at each in turn: Standard QPSK: With standard QPSK, each of the signal points are in quadrature (Note that the signal points in the constellation can be at any arbitrary phase really; ...
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8 votes

Why not use zero-signal in digital transmission?

All implementation aspects aside, the constellation you propose performs worse than QPSK in an additve white gaussian noise (AWGN) channel. I claim this based on simulations that I have run with ...
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8 votes

Transmit data through sound between 2 computers (very close distance)

As you have realized, the hard part of doing digital communications is carrier, symbol and frame synchronization, and channel estimation/equalization. The bad news is that you can't get around these ...
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8 votes

Why can so little digital information be stored on a cassette tape?

High-capacity tape formats use helical scanning. Here I look at why that gives a higher capacity than linear recording with four tracks (one stereo track on each side) like in a compact cassette (C-...
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8 votes

I'm missing something when it comes to understanding FM

In addition to the perspective offered in @Ash's answer, Claude Shannon touches on FM in his paper "Communications in the Presence of Noise" (Proceedings of the IRE, January 1949). He ...
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7 votes

FSK and IQ modulation

What is the advantage of performing the FSK using IQ modulation? You only need one RF oscillator operating at a single frequency, instead of having 2 (or more in the case of M-ary FSK) oscillators ...
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7 votes
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What is a constant envelope modulation?

You've pointed out a very important distinction between theory and practice. In theory, as suggested by your book and in Fat32's answer, modulation schemes where all information resides in the phase ...
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6 votes
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Real and complex low pass equivalent of band-pass signal

It's not true that any real-valued band pass signal can be written as shown in your first equation: $$s(t)=A(t)\cos(\omega_c t)\tag{1}$$ The most general representation of a real-valued band pass ...
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6 votes
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Why upsample before modulation?

The reason is aliasing. Because the modulation is digital, on the discrete signal, the sampling frequency should be high enough that the channel's frequency band does not extend beyond the Nyquist ...
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6 votes

Audio frequency modulation algorithm

You need to build a time varying delay, where you can modulate the delay amount over time. The peak delay modulation is a function of your maximum desired frequency shift and the modulation ...
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6 votes
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Gardner Timing Recovery for Repeated Symbols

Your Gardner Loop would properly "Flywheel" in the absence of symbol transitions. So it would slowly drift off of synchronization, but would not spiral out of control as you describe. This is ideal ...
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6 votes

How is multiplexing achieved in spread-spectrum modulations like CSS?

disclaimer Because of the lack of document about LoRa CSS in Internet, the analysis below may be wrong with respect to LoRa system, not to the (linear) CSS principle. Any comment or update are ...
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6 votes

Why do SDR receivers emit I/Q samples?

The SDR (or any general digital signal processing system) takes the received RF signal, and downconverts it from the carrier frequency to the baseband. Now, the real bandpass signal from the antenna ...
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6 votes

Average bit error and symbol energy

The optimal decision regions are the Voronoi Regions. I dont know, if this is what you are looking after. ...
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6 votes

Average bit error and symbol energy

As explained in Maximilian Matthé's answer, the exact computation of the symbol error probability of this constellation (ITU-T V.29 modem standard) is quite complex. However, you can quite easily ...
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What is the meaning of channel capacity?

1) Is there a connection between the modulation kind and the channel capacity? The capacity of a channel indicates the upper limit of how many bits can be transmitted per second over the channel with ...
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What is the meaning of channel capacity?

1) Is there a connection between the modulation kind and the channel capacity? Channel capacity is usually defined as the number of information (usually measured by the number of bits) can be sent ...
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6 votes
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Conversion between Eb/N0 and SNR in spread-spectrum modulation like LoRa CSS?

Let's start by fixing a symbol rate $R_s$ symbols per second. To modulate $R_s$ symbols per second without ISI, Nyquist says that we need a bandwidth at least $BW_0=1/R_s$ Hz. With spread spectrum, ...
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6 votes
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Difference between Line Code and Keying

I think the Wikipedia definition is limited, and anybody using the terms keying and line coding interchangably is wrong. A line code is an encoding (or mapping) from bits to pulse amplitudes (...
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6 votes
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Difference between FFSK and FSK modulation schemes

Fast FSK is just another term for minimum-shift keying (MSK). In the modern literature, the term fast FSK has been almost completely replaced by MSK. There is a very good tutorial paper on MSK by S. ...
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5 votes
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Really basic question about OFDM

Either of your suggested approaches would work (adapting modulation/coding scheme on a per-subcarrier basis or changing all subcarriers at once). There's no theoretical constraint that prevents you ...
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