# Tag Info

43

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, durability, ...) and isn't ever "universally true". I can see, for example, that "large" is already a relative term, and for a small office, the ...

10

You need to integrate the modulating signal because frequency is the time derivative of phase. Therefore, the typical relationship from introductory calculus holds: $$\phi_i(t) = \int_{-\infty}^{t} \frac{d\phi_i(\tau)}{d\tau} d\tau = \int_{-\infty}^{t} 2\pi f_i(\tau) d\tau$$ For causal signals, the lower limit on the integral changes to zero: $$\phi_i(... 6 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 operating at separate frequencies for each bit/symbol. Since you only have one oscillator, you don't have to worry about discontinuities in the phase of the ... 6 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-cassette). Figure 1. Stereo C-cassette player/recorder linear head (left) and a helical scanning head from a data drive (right), same scale. There is a too-short-... 5 Wow, I'm honored by Matt L. doing what I'm often doing: Referring people to GNU Radio. The project actually has a list of recommended literature, but I don't know how well that'd fit you. It's probably still worth looking into. Then, regarding QPSK: Well, it's one of the basic constellations, and you'd probably be best off reading a textbook intro to ... 5 First, the answer to why you do not see a negative voltage is that the output being digital will range from 0 to the maximum digital voltage at the output (+Vs). This will have a DC offset of +Vs/2 which is simply filtered out with a high pass filter (series cap) resulting in a bipolar waveform with negative voltage after the series cap. UPDATE: Based on ... 5 Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and receive radio signals. This question is ill-defined – a signal doesn't use quadrature modulation/demodulation, transmitters/receivers do. So, your question is, if we try to "rescue" it, is Do modern FM receivers/... 5 I waited a bit to see if someone else takes the challenge, but since there are no answers yet, I'm providing mine now. 5 In general, it means several waveforms will coexist in 5G ecosystem. In the context of LTE-based 5G (up to now), several subcarrier spacings (hence CP) coexist. The first and foremost motivation for this is to support not only mobile broadband but also other use-cases such as mMTC and URLLC. Some of benefits of mixed numerology are flexible scheduling and ... 4 If t is time, s(t) is the (appropriately scaled) signal, \omega_0 is the angular frequency, and \phi_0 is a phase offset, then phase modulation is$$ t \mapsto \sin(\omega_0 t + \phi_0 + s(t))  Different signs for $s(t)$ and/or $\phi_0$ may be used, depending on conventions and context. Frequency modulation is more complex to write down, because ...

4

How about just using $\dfrac{d\phi}{dt}$ to compute the instantaneous frequency? GNU Octave code (I just made up a sample rate of 2 Msps): pkg load signal; x = csvread('nonlinear_freq_fit.csv'); y = hilbert(x); z = y - mean(real(y)); dphi_dt = diff(unwrap(arg(z))); Fs = 2e6; f_inst = (Fs/2)/pi * dphi_dt; k = [0:length(f_inst)-1]; t = k/Fs; plot(k, f_inst); ...

4

This could happen as discriminator gain is increased with a filter discriminator approach since in many of those approaches the gain would be maximum and linear for small signals only and then the slope of the discriminator slowly goes down coinciding with the results in your plot (such that you no longer get a perfect sine wave out for a sine wave in—- so ...

4

Typical cheap cassette tape recorders and players in the 1970's used audio circuitry that did not have a completely flat frequency response and added a lot of phase distortion (mostly inaudible to most consumers). In addition, the computers did not use high sample rate low quantization DACS and ADCs (which cost a fortune back then), sometimes only a simple ...

4

You have already selected your answer, but I would like to put a few more lines. First of all, objecting to Marcus, I think that your first assumption is correct! We can store one hour of almost CD quality (14-16-bits, 44100Hz, stereo) analog audio into these commercial music casettes; i.e magnetic reels. So on a very rough basis you have almost a 600 MB (...

3

I just skimmed https://github.com/SaucySoliton/PiFmRds/blob/master/src/pi_fm_rds.c#L454 and from what that code looks like, it initializes a clock generator to run at an adjustable clock. Then, it uses the audio amplitudes to modify that clock's frequency in real time. PWM doesn't seem to be involved, aside from the program using the PWM unit to generate ...

3

Assuming an FM modulation of a sine wave of frequency $f_m$. Theoretically, the modulated signal is an infinite sum of cosines at the frequencies $f_c + nf_m$ ($n\in \mathbb{Z}$) which the amplitudes depend on the coefficients $J_n(\beta)$ (of course in addition to the amplitude of the carrier wave), where $\beta$ is the modulation index and $f_c$ is the ...

3

With GMSK the frequency modulation index is 0.5. With GFSK, the frequency modulation index is larger than 0.5 (the signaling tones are farther apart). The receiving techniques used for GMSK as an FSK work for GFSK.

3

There are many ways of demodulating the FSK signal Indeed! What is the advantage of performing the FSK using IQ modulation? Depends. Generally, IQ is the only shape you have your signal in, so using that is not much of a question – a direct downconversion system has IQ signals, and that's what you'll use. Using such a system has a lot of advantages, ...

3

What if they did all use the same carrier? What you're describing is a single-frequency network (SFN). These are in common use for things that are not stupid FM broadcast. The whole truth is that reception from different senders in an SFN just look like heavy multipath propagation, where the sent signal just takes multiple paths of different length to the ...

3

There's simply no inherent relation between carrier frequency and data rate. I assume a classical comms engineering education here, but since that most often introduces the concept of equivalent baseband early, a good explanation would be: This becomes obvious when you think about the complex baseband representation of a passband being the same, ...

3

I simply use unwrapped atan2(IQ(i)) - atan2(IQ(i-1)) to estimate a discrete derivative, then low pass filter to below 15 kHz. Although with a shallow slope, the 1st order approximation to atan() given by Boschen will work just as well. Your noise might be due to not unwrapping the phase delta, or to not low pass filtering after doing the phase ...

3

Frequency by definition is the derivative of phase with respect to time (a change in phase divided by the change in time is frequency). You see this with the radian expression for frequency given by $2\pi f$: A frequency of 1 Hz is 1 cycle per second which is $2\pi$ radians per second. So similarly phase versus time is the integral of frequency versus time. ...

3

That paper (1973) is about more natural, simple and rich audio synthesis using FM (which later became Yamaha's very populer FM synthesis audio chips). In that respect, the carrier frequency is taken very low compared to the modulating tone frequency, unlike in communication applications. Hence the the side lobes cross the zero frequency boundary and are ...

3

When generating the sine wave, the code uses a sampling frequency to establish discrete points in the time domain. It is not continuous. This means the wave is broken up into bins that are exactly 1/fs in size/width. So if you want a true integral of the wave, you have to take the average density of all the points in a bin by dividing by the sampling ...

2

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In U.S. broadcast FM, the various subcarriers (pilot tone, stereo L-R, RDS, etc.) are modulated into the upper sidebands (above the 15 kHz L+R/mono audio, but below 100 kHz, for instance 38 kHz DSB for the stereo subcarrier) of the baseband signal before that entire multiplex is used to wideband frequency modulate a single, much higher frequency, FM carrier....

2

Frequency is the derivative (or 1st difference) of phase. To get an IQ signal from which you can get phase angles, first multiply your wave file samples by a cosine at 3.15kHz and a sinewave at a frequency of 3.15kHz. That will hetrodyne your signal down to baseband IQ. Use atan2 of the IQ array to get an array of angles, take the 1st difference between ...

2

Yes. Pulse compression is really just running the returned signal through a pulse matched filter, which is equivalent to cross correlation. If you view it as a pulse matched filter, matched filters are optimal for detection of a signal in AWGN. If you view it as a cross correlation, the output of the correlation will peak when the signal best matches with ...

2

Checking the book you linked to, this equation refers to FM modulation over a (weakly) non-linear channel, modeled as a memoryless third-order non-linearity (Eq. 82). The third-order non-linearity produces signals at twice and at three times the carrier frequency $f_c$ (Eq. 84). Note that also the frequency deviations of these additional signal components at ...

2

Why not try your hand at working out the differences for yourself? Since you are interested in cosines, take, for example, the signal $x(t) = \exp(j(2\pi t + \theta))$ which is a complex sinusoid of period $1$ and sample it $16$ times per second to get $16$ samples $x[n]$, $n = 0, 1, \dots, 15$, where \$x[n] = x\left(\frac{n}{16}\right) = \exp\left(j\left(\...

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