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how to avoid aliasing

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am trying to write a function to check whether a list is sorted returning True or False. How can I avoid multiple variables pointing to the same thing?

EDIT : Please see this answer for the proper way to do it. I'll leave my answer here for posterity what's the correct way of handling this situation? To answer your specific question, you can use copy. However, a better method would be to use the sorted function to return a sorted copy of the list:.

how to avoid aliasing

Alternatively, you could make use of the sortedlist structure from blistthen your list will always be sorted. This is a very poor way, in terms of performance, to check that a list is ordered.

Digital Signal Processing/Sampling and Reconstruction

You should instead iterate over it checking that each element is greater or equal to the previous. Learn more. Avoid object aliasing in python? Ask Question. Asked 9 years, 3 months ago. Active 9 years, 3 months ago. Viewed 8k times. How can I avoid this? Johnny Johnny 2 2 gold badges 4 4 silver badges 6 6 bronze badges. This is -- perhaps -- the slowest way to do this.

The only thing which could be slower would be implementing your own version of sort. Lott Jan 6 '11 at There's something epistemological about the answers that involve sorting the list: it is completely unlikely that the program will have any use for a result different than True after the list has already been sorted. Besides, sorting an already sorted list is close enough to O nso Why bother querying, instead of just going ahead and calling sort or sorted? Active Oldest Votes.

It gives a sequence like [ L[0],L[1]L[1],L[2]It may be just nit-picking, but indexing a Python list should be much cheaper than slicing and zipping it.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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Digital Audio 101: What is Aliasing?

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Particularly, there is. The EWG issue is not yet resolved but apparently is considered ready for review. There is no question that the restrict qualifier benefits compiler optimization in many ways, notably allowing improved code motion and elimination of loads and stores.

So it seems like there is currently no good solution, although current compilers have extensions which offer C restrict like semantics there are a lot of grey areas section 3. The proposal mentioned N which mentions some of the techniques and flaws associated with these techniques.

how to avoid aliasing

For example:. This technique is both more complex and less efficient than simply passing the parameter by value. While the technique can be useful when dealing with legacy interfaces, it should not be a primary technique.

Note for interesting take on aliasing and the C99 restrict qualifier On the redundancy of C99's restrict.

If the intent is that you are not expecting size or a0. Now it is clear that you are intending to set all the elements to the same value.

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It is clear to the reader as well as the compiler. Learn more. How to avoid aliasing and improve performance? Ask Question. Asked 4 years, 9 months ago.

Sampling-Rate Conversion: Avoiding Aliasing During Downsampling

Active 4 years, 7 months ago. Viewed 2k times. Then my question is what should I do to the code to avoid the aliasing, and improve the performance? Pass a0 by value? But this will make a copying of a0 which I don't like, since in practice, class A may be very complex and copying is a very expensive option.

If yes, what is it? Allanqunzi Allanqunzi 2, 16 16 silver badges 43 43 bronze badges. I'm not too familiar with aliasing behavior but of what I'm reading, as long as the values that the function needs to read can be proven to the compiler not to be potential aliases of one another per the rules, it should avoid the overheads of refreshing the value each time.

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M Jul 24 '15 at MattMcNabb fair point, completely glossed over that Active Oldest Votes. For example: The simplest technique to overcoming aliasing is to copy the potentially aliasing parameter. This technique would apply to your case. Shafik Yaghmour Shafik Yaghmour k 27 27 gold badges silver badges bronze badges. Vaughn Cato Vaughn Cato Sign up or log in Sign up using Google. Sign up using Facebook.Digital sampling of any signal, whether sound, digital photographs, or other, can result in apparent signals at frequencies well below anything present in the original.

Aliasing occurs when a signal is sampled at a less than twice the highest frequency present in the signal. If an audio signal of containing a ultrasonic 45 kHz tone is sampled at The following figure illustrates what happens if a signal is sampled at regular time intervals that are slightly less often than once per period of the original signal. The blue curve is the original signal, and the red dots indicate the sampled values.

The red dots are what are recorded, since they represent the signal values at the times the signal is sampled. The pattern of the red dots is a terrible representation of the signal. The red sampled data looks like a sine wave at about one-tenth the frequency of the original! This is aliasing. Were nothing done to control aliasing, the effect on musical recordings would be devastating.

In the above case, the presence of an ultrasonic harmonic in the signal from the microphone would result in a low pitched tone present in playback. Signals at frequencies above half the sampling rate must be filtered out to avoid the creation of signals at frequencies not present in the original sound.

Thus digital sound recording equipment contains low-pass filters that remove any signals above half the sampling frequency. Aliasing can also cause problems in digital imaging. In images, the repetition is in space rather than time. If a repetitive pattern of high spatial frequency is sampled at low resolution, Moire patterns result. These are particularly troublesome when scanning half-tone magazine or newspaper photos, where the dot spacing may be as high or higher than the sampling frequency.

The phenomenon is most easily understood with a regularly repeating subject. In the discussion below, I have created aliasing using a "pixel resize" in Paint Shop Pro. The effect is the same as if one were to take a digital photo without antialias filtering. First, I started with an image of a brick wall. The original image is x Shown below is a small section of the original. A one-twelfth size image should look something like the following, with tiny individual bricks still visible barely but at one-twelfth size:.

However when I create a "pixel resize" the equivalent of taking a photo with no antialias filterI get the image shown below.

What is it aliasing? When it occurs?

The repeat pattern does not look much like bricks, and the most obvious repeat pattern vertically and horizontally is at a frequency very different from that of the bricks.

The tiny bricks are still in there, but they are nearly completely obscured by the dominant horizontal bands and bright dots that result from aliasing.The great attributes of discrete-time signals and systems rely on the ability to interface with the continuous-time domain.

Analog-to-digital converters ADCs and digital-to-analog converters DACs are the electronic subsystems that convert signals between continuous-time and discrete-time signal forms. This figure shows how to implement the interface of these two subsystems. The very first block of this figure represents the antialiasing filter. A higher-order filter design can help solve the leakage problem but only at the expense of a more complex analog low-pass filter.

A workaround to the complex analog filter is to start by oversampling the input signal. For audio signal processing, the factor may be 64 times the input signal or higher. With this configuration, the analog antialiasing filter can be low order.

Perhaps just a first-order low-pass filter — a resistor and a capacitor — is all your design needs for aliasing protection. Use a high-order digital filter, running at the oversampled rate, for precision antialias filtering, and combine this filter with a decimation operation, which brings the sampling rate back to a 1 times oversampling rate. The complexity of the high-order digital filter followed by a decimator is manageable by using a technique known as polyphase filtering, and the performance is good.

He is a member of the IEEE and is doing real signals and systems problem solving as a consultant with local industry.Earlier this year someone filed an income tax return using my identity. The topic of this blog post is aliasing, not tax fraud, although the concepts are similar. Aliasing in signal processing is when a sinusoid of one frequency takes on the appearance or identity of a different frequency sinusoid.

Similarly, aliasing is always a possibility when sampling a signal, and simple measures should be taken to prevent it from occurring. Signals, given the opportunity, will always alias. This post explores the basic reason for aliasing and considers a few examples.

The fundamental reason for aliasing of signals is the fact that discrete-time sinusoids are not unique functions of frequency. Sinusoids of frequency and are identical for all integers. For example. This property does not apply to continuous-time sinusoids because time is not limited to integers, but takes on a continuum of values. More on the properties of discrete- and continuous-time sinusoids is found in Sinusoidal Signals. Hence, discrete-time sinusoids are only unique over a interval of frequency.

Typically we work with the range of discrete-time frequencies. Aliasing of signals can occur when we sample - convert a continuous-time signal to a discrete-time signal. Continuous-time sinusoids with distinct frequencies are always unique. Consider two continuous-time sinusoids, and. These sinusoids have distinct frequency and thus are distinct. If two or more distinct continuous-time sinusoids contribute to the same discrete-time sinusoid, we have no way of distinguishing the original continuous-time sinusoids.

For example, if we observe that the amplitude of the discrete-time sinusoid at a particular frequency is 2, all we know is that the sum of an unknown number of continuous-time sinusoids produces an amplitude of 2. There are infinite combinations of continuous-time sinusoids that could sum to produce an amplitude of 2, and there is no way to uniquely determine their amplitudes.

The most common way to prevent aliasing is to limit the range of continuous-time sinusoids so there is a unique or one-to-one mapping between continuous- and discrete-time frequency.

This result immediately follows from the fact that see Sinusoidal Signals. This leads us to the Nyquist Sampling Theoremwhich states that there is a unique correspondence between discrete- and continuous-time sinusoids - no aliasing - if the sampling frequency is chosen to exceed twice the highest continuous-time frequency present in the signal. In this case one can uniquely reconstruct the continuous-time signal from its samples.

In practice the presence of noise and interference typically makes it impossible to know in advance the highest frequency present in the continuous time signal. A continuous-time low pass filter is applied to the data before sampling to limit the bandwidth to a desired range. This is called an anti-aliasing filter. The first example is a saxophone playing the note 'A'.We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services.

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For further information, including about cookie settings, please read our Cookie Policy. By continuing to use this site, you consent to the use of cookies. We value your privacy. Asked 11th Nov, Reginald Chellam. What is aliasing? Wind Tunnels. Most recent answer. Joe Zanter. TST Coatings. The data looked random and not meaningful to the process I was monitoring.

Upping the capture frequency was all it took. Once you see it, you'll hopefully! All Answers 6. Gianluca Argentini. Mathematics Nord Est Centre, Italy. Dear Reginald, aliasing is caused by discrete sampling below the Nyquist frequency. In order to recover the harmonics of shape in a signal, it is necessary to use a sampling rate at least twice the highest waveform frequency Shannon Theorem.

Abdelhalim Zekry. Ain Shams University. Aliasing is the folding of upper frequency part of an analog signal band on itself because of incorrect sampling operation. This results in the distortion of this part of spectrum.

This distortion must be prevented by using low pass antialiasing filter before sampling. The fold over can occur because when we sample an analog signal, multiple copies of the analog signal and their images result at fs, 2fs, 3fs, Consequently, sampled signal between 0 frequency and fs will have the original signal with maximum frequency fm and the reversed frequency image of the analog signal with its zero frequency at fs and its fm is below fs with fm.

The problem is that the real analog signals has long tails.

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These tails must be cut to limit fs since larger fs would lead to higher bit rate for the digital signal representation. It is the role of engineers to make the rate representing the signal as low as possible while preserving the signal undistorted. Best wishes. Ali K.Luckily, most audio engineers can spend their days being creative rather than having to worry about it. In other words, when a signal is sampled by a finite number of points, it cannot represent an infinite range of frequencies.

A conventional D-to-A converter for audio will only create signals within a specific frequency range that is determined by the sampling rate. If there are any recorded frequencies outside of this range, they are interpreted by the converter and mapped to frequencies within this range. This is aliasing — when one frequency is coded as a different frequency.

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The Nyquist frequency is the maximum frequency that can be recorded by a specific sampling rate. The Nyquist frequency is half of the sampling rate. When it comes to audio recording, if the sampling rate is 48, samples per second, the Nyquist frequency is 24, Hz. If the sampling rate is 44, samples per second, the Nyquist frequency is 22, Hz. If a signal contains any frequencies greater than the Nyquist frequency, they are interpreted by the converter and mapped to frequencies less than the Nyquist frequency.

Aliasing would be a big problem for digital audio, because it is usually not desired for frequencies to change in a signal. The good thing is that there is a dedicated component to prevent aliasing as part of the analog-to-digital and digital-to-analog conversion process. This component is called an anti-aliasing filter. Conceptually, the anti-aliasing filter blocks frequencies above the Nyquist frequency from being converted.

This is going to prevent any signals from changing frequency during the conversion process. In many car commercials, it appears as though the wheels on the car are rotating backwards while the car is traveling forwards. In reality, the car and the wheels are both traveling or rotating forwards.

Notice that a very fast rotation would actually be captured as a very slow rotation by the camera. Many audio signals are oscillatory in nature, meaning they repeat in cycles.

Unless a proper number of samples are recorded per cycle, the signal that represents with path of vibrating air molecules is not sufficiently represented. Search for:. Train Your Ears Premium Courses. Digital Audio What is Aliasing?

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