Frequency – Identify the three frequencies using the Fourier transform

The following simple function clearly has three frequency components:

 fun[x_] = Cos[ x] + Cos[2 x] + Cos[3 x];
data = Table[fun[x], {x, 0, 2 [Pi], 0.1}];
ListPlot[data, ImageSize -> 200]

How to show these frequencies using the Fourier transform? I tried the following

ListLinePlot[Abs[Fourier[data]], PlotRange -> All, ImageSize -> 200]

But that does not seem to lead to the right answer.

Edit: I would expect the Fourier diagram to show three peaks corresponding to three frequencies in the 1: 2: 3 ratio.

Fourier Analysis – FourierTransform Frequency

One of the methods is to adjust the FourierParameters

  FourierTransform(1, x, w, FourierParameters -> {0, -2*Pi})

Mathematica graphics

  FourierTransform(Exp(I a x), x, w, FourierParameters -> {0, -2*Pi})

Mathematica graphics


funs = {1, DiracDelta(x), Exp(I a x), Cos(a x), Sin(a x)};
result= {#, FourierTransform(#, x, w, FourierParameters -> {0, -2*Pi})}& /@ funs;
Prepend(result, {"f(x)","Fourier transform unitary, ordinary frequency"});
Grid(%, Frame -> All)

Mathematica graphics

With the second column of Wiki:

Mathematica graphics

hand luggage – Is it safe to travel with a radio frequency (RF) board packaged in a laptop carry-on?

In addition to a laptop,
I use a Radio Frequency (RF) card to implement a software-defined radio function (virtual e-node B or gNode-B, for example) with a small plug-in omnidirectional antenna.

Would that be a problem when going to an airport when it is packed in carry-on luggage and a laptop?

For information:
This is a USRP research group Ettus, National Instruments.

database design – How to model the frequency of events

In this brief discussion, I guess you are using a relational database. I am not a NoSQL guru!

It is best to ask the client what exactly he wants to capture and why. Abstract design and generic design lead to complexity in general.

The list of frequencies that you have provided is good, I think that by custom you want to address possibilities such as:

Of course, you would need a business rule to indicate what happens if that day is a holiday. This calls another holiday chart, so the program does not allow you to select such a day.

Managing such "bespoke" specifications is not easy, unless the variations are one-way specific.

In addition, there is a difference between "managing the meeting schedule" and "running the meeting." I guess in your example, you are mixing data for both (this may be correct depending on your needs).

When you schedule a meeting on Monday 9:00 every Mondaythis is what I mean by "meeting scheduling management", when the meeting was held (or canceled), the actual start time, end time, etc. . concern the specific instance of the meeting and do not affect the other table.

As a result, you have at least 2 main tables in the meeting area. One for the meeting schedule and another for the meeting (the many parties having a relationship of 0.1 or more).

A (meeting) must have a unique internal key. It has the date and the start time and the end date, the end time. The meeting can take place in a (location) or can be of (type) "virtual" if it is organized by telephone, for example. The meeting takes place between (parties), the meeting can have a (completion status) as planned, held, canceled, reprogrammed, etc. The meeting must have one or more (main discussion topics), and is usually intended for a specific group / section / project (Organizational Unit), and the analysis continues …

In the text above, the words between (…) are appropriate for the tables (of course, relations with the main meeting table must be respected).

In the meeting table, the columns that you display do not have to be as such. You can use the Timestamp data type with the SQL date functions to get almost all the necessary information. Unless the user accesses the table as is (as in a spreadsheet), you do not need to specify the columns that SQL Date functions might provide. I suggest you delete unnecessary attributes.

Personal note: It is interesting to note that there is at least one company in which we both work!

How to control the frequency of the ads?

This question was asked a moment ago and I wanted to check the current situation:

  • Can I control the frequency of ads since dashboard? (for example, frequency
    cap in Admob)
  • Can I control the frequency of ads via Unity API IAP?
  • If not, does that mean that I have to implement everything that "frequency
    feature manually?

android – How to generate and play a frequency with code?

My problem is that I want to create a frequency and reproduce it, but no matter what I look for in forums and others, I can not find an answer.
I have tried everything.

val duration = 10 // duration of sound
val sampleRate = 22050 // Hz (maximum frequency is 7902.13Hz (B8))
val numSamples = duration * sampleRate
val samples = DoubleArray(numSamples)
val buffer = ShortArray(numSamples)
var note :IntArray =  IntArray(buffer.lastIndex)

    var i :Int = 0
    while (i < buffer.lastIndex){

        samples(i) = Math.sin(2.0 * Math.PI * i.toDouble() / (sampleRate / note(0))) // Sine wave
        buffer(i) = (samples(i) * java.lang.Short.MAX_VALUE).toShort() // Higher amplitude increases volume

    var audioTrack = AudioTrack(
        sampleRate, AudioFormat.CHANNEL_OUT_MONO,
        AudioFormat.ENCODING_PCM_16BIT, buffer.lastIndex,

    audioTrack.write(buffer, 0, buffer.lastIndex)

What is the frequency of keywords?

Thank you for sharing your suggestions

is it important to use in SEO.

Thank you


Computational Linguistics – Theory of Information: Comparing Word Correction with a Variable Counting Frequency

It's a very broad question, I'm not sure that cstheory is the best place.

How can I compare the conditional surprise of words whose frequency varies?

$ S (w | context) = – log (p (w | context)) = – log ( frac {number (w, context)} {number (context)}) $

the $ account (w, context) $ depends on the frequency of the word w because this can be broken down into $ p (w | context) count (w) $. This means that a more frequent word will have a lower surprise.

Is there a way to compare the astonishment of words whose number / frequency varies, that is to say the control of the frequency? Did I just divide $ account (w, context) $ by $ account (w) $ normalize by number?

adnd – Is there a standard frequency for wandering monster controls in a dungeon?

Every three laps unless otherwise decided by the DM

This answer assumes that the only materials you use as reference are PHB, MM, and DMG.

How did I find this answer? (I hear people wondering) The 1st DMG is, as you pointed out in a commentary, organized in a counter-intuitive way.

You will find on page 190 the DMG under City meets the following text.

Check the encounters every three rounds as usual or otherwise as desired.

Where was the "normally" covered? Nowhere, although "once per turn" was "normally" for the original game (see below). Returning to "Keeping track of the weather" & # 39; on page 38, we find:

It is essential to keep an accurate record of the hour so that the deputy minister can determine when to check for stray monsters and to strictly control the duration of certain spells … He may happen that one party wants to hide. a long time maybe at night … that does not exempt them from occasional checks for wandering monsters, although the frequency may be somewhat moderate, according to the conditions …

Disconcertingly, for those looking for a concrete answer, a periodicity was suggested on page 174 …

When a random encounter is indicated by the periodic check …

But there is no hard and fast rule in this section on random monsters, and it also returns you to your own chart / chart in this passage. Which implies that you had better create your own graph and your own periodicity, but it does not require anything.

The 1st DMG AD & D is as usual, not going to give you a hard and fast rule. Do not let this be an obstacle to play. Throughout the 1st DMG AD & D, the author has devoted a significant amount of text to provide the DM the following indications that I will summarize in a simple principle: do what you want, you're the DM.

And it works. (Well, it worked for me for a few years when I ran and played in the AD & D dungeons 1e).

Alternative answer: Once per turn, roll 1d6

Many AD and D have been written with the basic assumptions of playing Original D & D (three little books in a box, 1974) as an integrated hypothesis. In Volume III, Adventures in the Desert and the Underworld, on page 10, we read:

Wandering monsters: At the end of each round, the referee rolls a six-sided die and sees if a wandering monster has been encountered. A score of 6 indicates that a wandering monster has appeared.


In all honesty, during the first five years I played at D & D and AD & D (1975-1981), this was "normal" in many of the dungeon crawls in which I participated .

Use wandering monsters to "get things done"

None of the above precludes the use of a Random Monster Check whenever you feel it is appropriate. With published adventures, some have a guide to random checks of monsters, others not.

Python – How can I have my FFT peaks, exactly at the frequency of my signal?

I've seen the code below here, but if you trace it and zoom it, the frequency peaks do not exactly match 50Hz and 80Hz; they are a little behind. Does anyone know why this happens? How to make the peak exactly at 50Hz and 80Hz?

import numpy as np
import matplotlib.pyplot as a plt
import scipy.fftpack

# Number of sampling points
N = 600
# sample spacing
T = 1.0 / 800.0
x = np.linspace (0.0, N * T, N)
y = np.sin (50.0 * 2.0 * np.pi * x) + 0.5 * np.sin (80.0 * 2.0 * np.pi * x)
yf = scipy.fftpack.fft (y)
xf = np.linspace (0.0, 1.0 / (2.0 * T), N / 2)

fig, ax = plt.subplots ()
ax.plot (xf, 2.0 / N * np.abs (yf[:N//2])) ()