## Normalizing the supernova spectrum by photometry

I have a SN spectrum here (already reduced) that seems to have some artifacts. Professor tells me that I may have to normalize it using photometry.
As far as I understand, I just have to multiply it by some factor to make the integral over all frequencies equal to bolometric luminosity. Am I right, or is there some more complicated thing here?

## What spectrum analyzer can detect Wireless AD?

Wireless AD now has a 60GHz frequency band. Because of its immense bandwidth, I’d like to measure, how much ElectroMagnetic Radiation I am exposed to when I am in its vicinity. However, the website dedicated to EMR measurement devices does not have anything that can measure over 18GHz. After searching around on the internet, even the most sophisticated, computer-linked spectrum analyzer only has capabilities up to 20GHz. Ironically, their company has an antenna which can amplify signal up to 35GHz. Still nowhere close to the 60GHz though. So few similar questions:

• Is there any spectrum analyzer that can measure frequencies higher than 20GHz?

• Is there anything that can measure up to 35GHz, making full use of their antenna?

• Is there anything that can measure Wireless AD signal strength? I read abstracts of articles where its levels were measured, but I don’t have access to the articles themselves, to see how these levels were measured.

## Why does the first peak of the temperature power spectrum of CMB imply a flat Universe?

According to Wikipedia, the first peak of the temperature power spectrum of CMB determines the curvature of the Universe. And this answer by @pela says that the first peak is consistent with a flat Universe. So my questions are how/why does the first peak tell us the curvature?

## Phase Modulation and Intermodulation Anomaly ? (Spectrum plots inside – **Updated**)

I have a MATLAB script for modelling a two tone signal (a sum of two sinusoids) going through a non linear transfer function (such as an amplifier). The amplitude of a signal is amplified non linearly, and also the phase is modified depending on the input power of the signal.

The two sinusoids used are at 20 Hz and 21 Hz.

With just amplitude modulation, the output spectrum looks as expected (first two plots) Its non linear so 3rd order and fifth order intermods can be seen around the frequency of the two sinusoids, aswell as harmonics. I know the amplitude modulation is correct because I obtain the correct third order intercept for the amplifier model. Upper graphs are in volts, lower graphs in dB Watts

However, when phase is adjusted depending on the input signal power, the spectrum looks like this… and my fifth order intermods are lost (again upper graph in volts, lower graph in dBW)

I have an idea but I am not confident with the explanation of this and was hoping someone with a trained eye can assist or offer advice

How its coded –> My script looks at each point on the input signal, reads its amplitude and adds a phase adjustment to it during reconstruction of the signal, as shown in the phase transfer plot below (which shows the effect the equipment will have on any signal going through it). So if the amplitude (input power) of the signal is -70 dBW then a phase of 0.01 radians is added to the reconstructed signal at that exact point… then it looks at the next sample point and adds a phase to that. So if the amplitude of the wave is at -70dBW then the reconstructed waveform is cos(2*pi*f + 0.01). Adding 0.01 in phase is an I and Q modulation when cos(2*pi*f + 0.01) is written with the trig identity to get the IQ form.

Confident I have not made any mistakes with unit conversion (again because third order intercept is correct).

Look at the input signal, output signal and the phase deviation added to the signal in time domain… it looks good

## Code for Generating Spectrum (MFCC) vs. Time Images

I am trying to do speech wake up (hot) word recognition by transforming it into an image recognition problem. The images are some kind of spectrum (MFCC) vs. time, made from a wave signal. I recall seeing publications on this approach but can’t find the code for this task. I would like to avoid a bloated and buggy Bazel/tensorflow solution. Any suggestions?

Thanks!

## Plot the spectrum and n-point DFT

$$x_a(t) = cos(2pi f_a t)$$ was sampled with sampling period $$T_s$$. Plot the { spectrum | $$N$$-point DFT } of $$x[n]$$ ($$f_a$$, $$T_s$$ or $$f_s$$ given, $$N$$ given – whole number of periods or not).

Anyone can help?

## (Sanity check) the adic spectrum \$operatorname{Spa}(mathbb{Z}, mathbb{Z})\$

I am following Scholze’s and Weinstein’s notes on $$p$$-adic geometry on http://www.math.uni-bonn.de/people/scholze/Berkeley.pdf, example 2.3.6 (page 18 as of this moment bar any updates).

$$operatorname{Spa}(mathbb{Z},mathbb{Z})$$ is the space consisting of points

• $$eta$$, sending all nonzero integers to $$1$$
• $$s_p : mathbb{Z} rightarrow mathbb{F}_p rightarrow {0,1}$$, where the second arrow sends all nonzero elements to $$1$$
• and $$eta_p : mathbb{Z} rightarrow mathbb{Z}_p rightarrow p^{mathbb{Z}_{leq 0}} cup {0}$$, where the second arrow is the $$p$$-adic absolute value.

One of the closed sets is then $$overline{{eta_p}} ={ eta_p , s_p}$$, let me call the complement of this $$U$$, which is an open set. The notes proceed to define two maps (where I have replaced $$R = mathbb{Z}$$ in the notes)

• $$textrm{Spec}(mathbb{Z}) rightarrow textrm{Spa}(mathbb{Z},mathbb{Z})$$, sending $$mathfrak{p}$$ to the valuation $$R rightarrow textrm{Frac}(R/mathfrak{p}) rightarrow {0,1}$$, and
• $$textrm{Spa}(mathbb{Z}, mathbb{Z}) rightarrow textrm{Spec}(mathbb{Z})$$, sending a valuation to its kernel.

Finally, the notes claim that (again I have replaced $$R$$ by $$mathbb{Z}$$)

if $$U subset textrm{Spa}(mathbb{Z},mathbb{Z})$$ is any open subset, the pullback along the composite $$textrm{Spa}(mathbb{Z},mathbb{Z}) rightarrow textrm{Spec}(mathbb{Z}) rightarrow textrm{Spa}(mathbb{Z},mathbb{Z})$$ is a subset $$V subset textrm{Spa}(mathbb{Z},mathbb{Z})$$ with $$V subset U$$.

My question: So I have tried to plug in the example where $$U = textrm{Spa}(mathbb{Z},mathbb{Z}) – {eta_p, s_p}$$ (as defined above), and I seem to arrive at $$V= textrm{Spa}(mathbb{Z},mathbb{Z}) – {s_p}$$, which contradicts what I should have expected. What went wrong?

I have worked out that (which is possibly incorrect) the first map $$textrm{Spec}(mathbb{Z}) rightarrow textrm{Spa}(mathbb{Z},mathbb{Z})$$ sends $$0$$ to $$eta$$ and $$(p)$$ to $$s_p$$, and the second map $$textrm{Spa}(mathbb{Z},mathbb{Z}) rightarrow textrm{Spec}(mathbb{Z})$$ sends $$eta mapsto 0$$, and $$s_p mapsto (p)$$, and $$eta_p mapsto 0$$.

Remark: the notes finally proceed to claim that

In particular, any open cover of $$textrm{Spa}(R,R)$$ is refined by the pullback of an open cover of $$textrm{Spec}(R)$$

which to me suggests that it’s not simply a misprint on the notes, that’s why I would like to clear up the confusion I am having.