Questions tagged [frequency-modulation]

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24
votes
6answers
7k views

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. So I figured I can store a relatively large amount of data on a cassette tape. I was thinking of a little project to ...
6
votes
2answers
688 views

Why do we integrate the modulating function in FM?

I've been reading about FM and I keep coming to an expression, where the instantaneous phase $$\Theta=2\pi f_it+\phi\text, \tag1$$ where $$f_i=f_c+k_fm(t)\text,\tag2$$ ($f_c$ being the base carrier ...
3
votes
2answers
6k views

FSK and IQ modulation

I am having trouble understanding the FSK modulation process. There are many ways of demodulating the FSK signal. What is the advantage of performing the FSK using IQ modulation? How to demodulate ...
3
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1answer
353 views

Simulation of a Frequency ramp

This might be an easy one! Please preface your answer with spoiler notation by typing the following two characters first ">!" Given the following equation that describes a cosine wave as a function ...
3
votes
1answer
83 views

Positive slope of BER with a greater frequency deviation?

I am trying to implement a frequency-modulated communication channel on MatLab. However, there is something I don't understand about the sensitivity of the frequency modulator (or the frequency ...
3
votes
1answer
176 views

How to estimate the frequency characteristics of a nonlinear chirp?

Given a partial time-domain recording of a noise-corrupted chirp that asymptotically approaches a frequency, and the function that determines the non-linearity, how can I accurately estimate the final ...
3
votes
1answer
131 views

Fourier transform of frequency division

I need a mathematical description of what happens to the spectrum of a signal when that signal is processed to divide its frequency. As an example, construct an input signal as the sum of two sine ...
2
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2answers
827 views

How does the RaspberryPi radio hack convert digital GPIO signals to an FM signal?

After having looked at various explanation of how the RaspberryPi FM transmitter hack works, I realize there are some fundamental pieces missing. Most explanations talk about how to construct a ...
2
votes
1answer
248 views

Recommendation for good ressources on digital processing and D-QPSK

I've been a C++ developer for 10 years. Quite high level. And I am completely new to Digital Signal Processing. I am trying to implement a Software Defined Radio. Specifically I am trying to receive ...
2
votes
2answers
103 views

Power of an angle-modulated wave

Let $$\phi(t) = A\cos(\omega_c t + km(t)) \tag{1}$$ be an angle-modulated wave(FM or PM). What's the power of $\phi(t)$? Intuitively, it seems that the answer is $$P = \frac{A^2}{2} \tag{2}$$ since ...
2
votes
1answer
2k views

How to convert sampled real audio signal to it's IQ components for IQ modulation?

So my question is this: How to convert sampled real audio signal to it's IQ components for IQ modulation? For instance: WHen I have my DSP or FPGA receive a audio signal through a ADC, which is just ...
2
votes
1answer
794 views

About phase unwrapping

I am not too familiar with phase-related problems so I need some suggestions or corrections in a problem that might be an old but easy one. Here is my problem: given a complex signal: $$y(t) = e^{j\...
2
votes
1answer
275 views

What's the relationship between the parameters of this noise generator and the gaussian curve it produces in the frequency domain?

This algorithm produces a sequence $y$ having a magnitude spectrum that resembles a normal distribution, peaking at frequency $\omega$: $$b[n]=(1-\sigma)b[n-1]+\frac{\sigma}{\omega} C$$ $$p[n]=p[n-1]+...
2
votes
2answers
699 views

FM signal detection

I'm just playing around with cheap RTL based SDR dongle and I wanted to implement a simplistic FM radio receiver. I managed to get mono sound with no problem, however I decided to implement automatic ...
2
votes
1answer
1k views

Hilbert Transform of an FM Signal

The Hilbert Transform of an Amplitude Modulated signal returns the envelope of the signal. What does the Hilbert transform of a Frequency Modulated signal return? How can I use the Hilbert Transform ...
1
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2answers
2k views

Quadrature modulation for FM and AM

This might be a naïve question, are these correct statements? Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and ...
1
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2answers
2k views

How does complex data of an FFT and IQ modulation differ?

If I have an arbitrary time domain signal (e.g. a simple cosine) i can sample it with an ADC and get a time discrete representation. I can perform an FFT on the samples and get a complex output. The ...
1
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1answer
495 views

Simplified equations for FM (frequency modulation) synthesis and PM (phase modulation)?

Clicking on the links I find on the web it seems many authors don't express them neatly enough for me or they're even confusing the two. Can someone please clear this up? Is frequency modulation \...
1
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3answers
55 views

Can the intelligence message of an FM signal be cross-modulated to another center frequency due to non-linearities?

Can the intelligence message of an FM signal be cross-modulated to a a different frequency by non-linearities, but with the FM modulating message remaining (relatively) intact on the new frequency? ...
1
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1answer
37 views

FM: Do rational ratios of carrier to modulator signals really produce harmonic spectra?

I've read that in FM, all rational ratios of the carrier frequency to the modulator frequency produce harmonic spectrum in the FM signal. Link to what I read. I don't understand why this is. If for ...
1
vote
1answer
357 views

How is frequency related to data rate?

How does (if it does) frequency affect/relates to Data Rate. Why for example using the same modulation, LoRa (in the physical layer), you get somewhere around 250kbps at 2.4Ghz and only 20kbps at ...
1
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1answer
2k views

difference between GMSK (Gaussian Minimum shift keying) and GFSK (Gaussain frequency shift keying) [closed]

I am unable to differentiate GMSK and GFSK. How do the modulation techniques differ in Tx? How do their receiving techniques differ..?
1
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2answers
1k views

Impact of modulation index in FM

If I have the spectrum of a FM modulation, does the frequency of the carrier disappear when the modulation index is too big? Does the amplitude of any side band depend from the modulation index? And ...
1
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2answers
2k views

IQ FM Demodulation of Wow and Flutter Signal in Software

Background: I have a recording device that exhibits Wow and Flutter, or periodic frequency deviation. I use this device to record a calibrated 3.15kHz test tone from a tape film to generate a .wav ...
1
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1answer
126 views

Frequency response of FM modulation/demodulation chain with phase derivative demodulation

Frequency modulating a carrier by white noise and then demodulating the complex signal using discrete derivative of phase it appears that the discriminator is acting as a low-pass filter. How do I ...
1
vote
1answer
168 views

Frequency modulation implementation without trig functions

https://dsp.stackexchange.com/a/1087 This answer suggests generating a sine wave using complex phasor multiplication. At each step the phasor is multiplied by another complex number (omega) to rotate ...
1
vote
1answer
2k views

FM demodulation with arctan

I am trying to demodulate a FM signal with a RTL-SDR and python using the arctan method. From here I know that $$ \frac{d}{dt}\arctan(\frac{q(t)}{i(t)}) = \frac{i(t)\frac{d}{dt}q(t)-q(t)\frac{d}{dt}i(...
1
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1answer
251 views

Frequency modulation of $m(t)$ in MATLAB

I have a message signal defined in the below interval $$ m(t)=\begin{cases}1&, 0\leq t < \frac{t_0}{3}\\[2ex] -2&, \frac{t_0}{3}\leq t <\frac{2t_0}{3}\\[2ex] 0&, \frac{2t_0}{3}\leq t ...
1
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2answers
1k views

How to Design a Pre-emphasis filter knowing the gain, a zero and a pole?

I am simulating an FM radio signal in order to use it as a waveform in passive radar; for this purpose I'm following an article: Analysis and Emulation of FM Radio Signals for Passive Radar In a ...
1
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1answer
75 views

How does the earphone cable in a mobile phone pick up the FM reception?

As I understand, the RF frequency-modulated signal centered in the range of $88-108\textrm{ MHz}$, is picked by the earphone antenna and is directly sampled by the sound card adc at $48\textrm{ kHz}$ ...
1
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1answer
46 views

Convert old computer cassette signal into binary

Completely new to this but keen to learn :) I have an old BBC Micro computer cassette which I've recorded into unsigned 8-bit pcm wav file format. The file comprises tracks separated by virtual ...
1
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1answer
40 views

What does the variable $\tau$ mean in frequency modulation?

Frequency modulation formula: $$ x_{FM}(t) = A_{c}\cos\left(2\pi f_{c} t+ 2\pi k_{f}\displaystyle\int_0^{t}m(\tau)d\tau+\phi_{0}\right) $$ Its change from $m(t)$ to $m(\tau)$. What is $\tau$? I wonder ...
1
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1answer
27 views

Signal distortion under non-linear channel

The channel is given to have these characteristics, and its required to study the affect on Frequency Modulated signal and its demodulation. Since there are no sharp corners (like during clipping) ...
1
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1answer
27 views

RF Downconversion using Heterodyne Principle

after a RF down-conversion using heterodyning principle, will there be an information loss? If we translate to a fixed IF frequency, is there is an intuitive way of explain that the information can be ...
1
vote
1answer
231 views

FM modulation audio 50 Hz – 16 kHz MATLAB

I'm trying to modulate in FM an audio signal $x(t)$ coming from a microphone which works from 50 Hz to 16 kHz in MATLAB. But the problem is that I want a FM Bandwidth of 25 kHz at the output of ...
1
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2answers
808 views

Formula of frequency modulated sine wave from data points

I'm trying to determine the formula of a variable frequency sine wave based on the values of max1, max2, min1 and min2. y(0) isn't necessarily 0 and I can assume the frequency increases or decreases ...
1
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1answer
420 views

Biquad cookbook formula for broadcast FM de-emphasis?

Can a simple IIR biquad filter be used as an audio de-emphasis filter for broadcast FM radio? If so, how does one translate the filter requirements (50 uS time constant in the U.S.?) into parameters ...
1
vote
1answer
863 views

How to express FM and PM the most simple way?

I'm trying to understand how to tell phase modulation from frequency modulation by looking at their respective expressions, simplified, particularly frequency modulation. Also, it would be nice for ...
1
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0answers
139 views

Wideband FM bandwidth estimation

In the book Modern Digital and Analog Communication Systems by B. P Lathi, there is a section for the estimation of WBFM bandwidth. First, the staircase approximation of $m(t)$ is constructed by the ...
1
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0answers
39 views

Non-coherent FSK and Orthogonality and square-law detectors

This is a basic figure that explains how Non-Coherent FSK actually works. The incoming signal $ r (t)=\sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$ where P denotes the signal power in ...
1
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0answers
33 views

Instantaneous frequency, PLLs, frequency mixing, cross-correlation and the cross-correlation matrix

This is as much a request for comment and critique as anything else. I am looking at tracking how a system perturbs an input that is a (real) sinoid of varying frequency. ...
1
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1answer
423 views

Digital FM Demodulation

I have created a Common Lisp Library to receive samples of an FM signal from BladeRF1 SDR. I want to write a subroutine to implement FM demodulation. The input should be in the format of IQ data. ...
1
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0answers
42 views

Help in identifying low speed image transmission protocol over RF

In the seventies I worked for Muirhead on press fax machines that used to transmit pictures over radio and landline as I recall two FM systems were used a carrier 800 Hz modulated +- 150 Hz and 1900Hz ...
1
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0answers
457 views

Spectrum of WBFM signal for triangular message signal spectrum

We Know: Frequency Modulated signal is given by: $$s_{FM} (t)=A_{c} \sin \{ w_c t + 2 \pi k_f \int m(t) \, dt \}$$ Now, if $ \quad m(t)= A_m \cos(w_m t)$ , i.e, its spectrum $M(f)$: then, $$s_{FM} (t)...
1
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0answers
436 views

Best Way to Extract Frequency from Signal [closed]

I want to send signal that compound from 16 different frequency over GSM. The problem is the GSM network is very noisy and I have only 400-3400 hz frequency available for use. I try using fft ...
1
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1answer
979 views

How to generate IQ component for transmitting 2FSK

I am trying to generate IQ components for 2FSK modulation. I have started off from this thread FSK and IQ modulation , but I don't quite understand the IQ TX components plotted in the example there by ...
1
vote
0answers
134 views

low-frequency amplitude with phase modulation of low Hz carrier

I am writing an FM/PM synthesizer, using Java. For the most part it works pretty well. What I am curious about is an attempt to use a low frequency tone as a carrier. By low frequency, I mean in the ...
1
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0answers
68 views

Angle harmonic distortion in FM modulation

As you know the output form of FM modulator is something like this: $$s(t)=A_{C}\cos(2\pi F_{c}t+\beta \sin(2\pi F_{m}t))$$ where $\beta$ is the phase deviation. I want to know why in this book the ...
1
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0answers
237 views

Calculating amplitudes of FM Sidebands

How are the amplitudes of FM sidebands calculated? E.g. when negative frequencies are reflected back and their amplitudes added to any existing positive frequencies at that band, how are the ...
0
votes
4answers
406 views

How to isolate overlapping FM signals?

Analogue radio stations often have a range of frequencies that they can use. Different transmission towers will transmit on different carrier frequencies in this range, because the signal takes time ...