What is the meaning of high or low frequency for digital signal.( I think this is not related to sampling frequency right?) For example, we have an array and its size is 10. How can I understand whether that 10 numbers represent high or low frequency? Thanks.
Idea of high or low frequency for digital signal
Started by ●August 24, 2009
Reply by ●August 24, 20092009-08-24
On Mon, 24 Aug 2009 13:43:58 -0700, rotor cli wrote:> What is the meaning of high or low frequency for digital signal.( I > think this is not related to sampling frequency right?) > > For example, we have an array and its size is 10. How can I understand > whether that 10 numbers represent high or low frequency? Thanks.You mean "sampled signal?" A "digital signal" would be one that takes on the values 0 or 1. If you analyze the array for it's energy content vs. frequency, and most of the energy is concentrated at low frequencies, then it's a low frequency signal, and visa versa. -- www.wescottdesign.com
Reply by ●August 24, 20092009-08-24
On 25 Ağustos, 00:10, Tim Wescott <t...@seemywebsite.com> wrote:> On Mon, 24 Aug 2009 13:43:58 -0700, rotor cli wrote: > > What is the meaning of high or low frequency for digital signal.( I > > think this is not related to sampling frequency right?) > > > For example, we have an array and its size is 10. How can I understand > > whether that 10 numbers represent high or low frequency? Thanks. > > You mean "sampled signal?" A "digital signal" would be one that takes on > the values 0 or 1. > > If you analyze the array for it's energy content vs. frequency, and most > of the energy is concentrated at low frequencies, then it's a low > frequency signal, and visa versa. > > --www.wescottdesign.comI meant discrete time signal that has 10 numbers. I am just trying to understand frequency concept for discrete signal. What makes these 10 numbers high or low frequency?
Reply by ●August 24, 20092009-08-24
On Aug 24, 3:43�pm, rotor cli <rotor...@gmail.com> wrote:> What is the meaning of high or low frequency for digital signal.( I > think this is not related to sampling frequency right?)Not right. :(> For example, we have an array and its size is 10. How can I understand > whether that 10 numbers represent high or low frequency? > Thanks.Ask youself what would happen if you sampled a 1-volt 1GHz sine wave at sample rate of 1Gs/s, each time when wave is at its maximum (upper hump), 10 samples. Your array would contain 10 values of 1. You would get the exact same array of 10 values if you sampled a 1-volt 1Hz sine wave at 1s/s. Which of these samples represent your high-frequency signal and which represents the low-frequency signal? It is not meaningful to digitize a signal without regard for what you did when you digitized the signal. -Le Chaud Lapin-
Reply by ●August 24, 20092009-08-24
On Mon, 24 Aug 2009 14:55:03 -0700, rotor cli wrote:> On 25 Ağustos, 00:10, Tim Wescott <t...@seemywebsite.com> wrote: >> On Mon, 24 Aug 2009 13:43:58 -0700, rotor cli wrote: >> > What is the meaning of high or low frequency for digital signal.( I >> > think this is not related to sampling frequency right?) >> >> > For example, we have an array and its size is 10. How can I >> > understand whether that 10 numbers represent high or low frequency? >> > Thanks. >> >> You mean "sampled signal?" A "digital signal" would be one that takes >> on the values 0 or 1. >> >> If you analyze the array for it's energy content vs. frequency, and >> most of the energy is concentrated at low frequencies, then it's a low >> frequency signal, and visa versa. >> >> --www.wescottdesign.com > > I meant discrete time signal that has 10 numbers. I am just trying to > understand frequency concept for discrete signal. What makes these 10 > numbers high or low frequency?I told you. But to give an example, if it goes 1,1,1,1,1,1,1,1,1,1 it has all of its energy at frequency = 0, while if it goes 1,-1,1,-1,1,-1,1,-1,1,-1 then it has all of its energy at frequency = 1/2 sample rate. (Note that there's not too many possibilities with just ten samples -- the Nyquist rate is at 1/2 the sample rate and can't be changed, there's only three well-defined frequency steps between that and DC). -- www.wescottdesign.com
Reply by ●August 24, 20092009-08-24
On Mon, 24 Aug 2009 14:55:03 -0700, rotor cli wrote:> I meant discrete time signal that has 10 numbers. I am just trying to > understand frequency concept for discrete signal. What makes these 10 > numbers high or low frequency?This is a basic question, so you can start with looking at simple discrete sine signals - which are the "single frequency" signals. [The following are some musings which are not very strict but I hope would be helpful.] Roughly speaking, frequency - analog or discrete - means how fast a periodic signal "repeats" itself (goes from one period to another). With a discrete sine, its frequency also tells you *how fast* it may *change its value* between two consecutive samples. With analog signals, increasing a sine's frequency increases the maximal value of its derivative [recall: the derivative of sin(w*t) is w*cos (w*t)]. Here with discrete signals, it increases the maximal difference of value a sample can have with a previous one [won't go into big maths here]. So either way, the frequency essentialy tells you the pace of change, whatever the mathematical details (derivative / difference). A constant digital signal - a series of the same value, e.g. 0 - can be interpreted (similarly as a constant analog signal) as a zero-frequency (co)sine: cos(0 * n) , where n is the sample number. It's constant, its value doesn't change, so the frequency of its changes (oscillations) is zero. As you look at discrete sines with an increasing frequency, you would get a signal that switches from +1 to -1 going through zero (+1, 0, -1, 0, +1, 0 and so on), which is really: cos(pi/2 * n) , where n is the sample number. So, it's a (co)sine signal with the angular frequency of pi/2. This means its "physical", temporal frequency is a quarter of the sampling frequency (2*pi / 4 = pi/2, where 2*pi corresponds to the sampling frequency). The most rapidly changing discrete signal is +1, -1, +1, -1 and so on -- switching from the most positive value to the most negative value (and back) every one sample. This is really: cos(pi * n) , which means a half of the sampling frequency. This is the Nyquist frequency mentioned in the sampling theorem. You just can't get more rapid changes than in a series of alternating +/-1, or more generally, +/- amplitude. Now for more complicated signals, it's usually a matter of applying a Discrete Fourier Transform to present the signal as a sum of separate sine (or more generally, complex exponential) components - quite similarly to continuous-time Fourier transforms, which you probably know. Regards, -- Krzysztof Lubański
Reply by ●August 25, 20092009-08-25
On 25 Ağustos, 02:42, Krzysztof Lubański <lu...@nerdshack.com> wrote:> On Mon, 24 Aug 2009 14:55:03 -0700, rotor cli wrote: > > I meant discrete time signal that has 10 numbers. I am just trying to > > understand frequency concept for discrete signal. What makes these 10 > > numbers high or low frequency? > > This is a basic question, so you can start with looking at simple > discrete sine signals - which are the "single frequency" signals. > > [The following are some musings which are not very strict but I hope > would be helpful.] > > Roughly speaking, frequency - analog or discrete - means how fast a > periodic signal "repeats" itself (goes from one period to another). With > a discrete sine, its frequency also tells you *how fast* it may *change > its value* between two consecutive samples. > > With analog signals, increasing a sine's frequency increases the maximal > value of its derivative [recall: the derivative of sin(w*t) is w*cos > (w*t)]. Here with discrete signals, it increases the maximal difference > of value a sample can have with a previous one [won't go into big maths > here]. So either way, the frequency essentialy tells you the pace of > change, whatever the mathematical details (derivative / difference). > > A constant digital signal - a series of the same value, e.g. 0 - can be > interpreted (similarly as a constant analog signal) as a zero-frequency > (co)sine: > > cos(0 * n) , > > where n is the sample number. It's constant, its value doesn't change, so > the frequency of its changes (oscillations) is zero. > > As you look at discrete sines with an increasing frequency, you would get > a signal that switches from +1 to -1 going through zero (+1, 0, -1, 0, > +1, 0 and so on), which is really: > > cos(pi/2 * n) , > > where n is the sample number. So, it's a (co)sine signal with the angular > frequency of pi/2. This means its "physical", temporal frequency is a > quarter of the sampling frequency (2*pi / 4 = pi/2, where 2*pi > corresponds to the sampling frequency). > > The most rapidly changing discrete signal is +1, -1, +1, -1 and so on -- > switching from the most positive value to the most negative value (and > back) every one sample. This is really: > > cos(pi * n) , > > which means a half of the sampling frequency. This is the Nyquist > frequency mentioned in the sampling theorem. You just can't get more > rapid changes than in a series of alternating +/-1, or more generally, +/- > amplitude. > > Now for more complicated signals, it's usually a matter of applying a > Discrete Fourier Transform to present the signal as a sum of separate > sine (or more generally, complex exponential) components - quite > similarly to continuous-time Fourier transforms, which you probably know. > > Regards, > -- > Krzysztof LubańskiOK. Thanks for all. So; for example we have a picture and an array that represents its RGB values of pixels. Can we say how much RGB values of pixels are irrelevant it has a high digital frequency and vice versa.
Reply by ●August 25, 20092009-08-25
On 25 Ağustos, 12:34, rotor cli <rotor...@gmail.com> wrote:> On 25 Ağustos, 02:42, Krzysztof Lubański <lu...@nerdshack.com> wrote: > > > > > On Mon, 24 Aug 2009 14:55:03 -0700, rotor cli wrote: > > > I meant discrete time signal that has 10 numbers. I am just trying to > > > understand frequency concept for discrete signal. What makes these 10 > > > numbers high or low frequency? > > > This is a basic question, so you can start with looking at simple > > discrete sine signals - which are the "single frequency" signals. > > > [The following are some musings which are not very strict but I hope > > would be helpful.] > > > Roughly speaking, frequency - analog or discrete - means how fast a > > periodic signal "repeats" itself (goes from one period to another). With > > a discrete sine, its frequency also tells you *how fast* it may *change > > its value* between two consecutive samples. > > > With analog signals, increasing a sine's frequency increases the maximal > > value of its derivative [recall: the derivative of sin(w*t) is w*cos > > (w*t)]. Here with discrete signals, it increases the maximal difference > > of value a sample can have with a previous one [won't go into big maths > > here]. So either way, the frequency essentialy tells you the pace of > > change, whatever the mathematical details (derivative / difference). > > > A constant digital signal - a series of the same value, e.g. 0 - can be > > interpreted (similarly as a constant analog signal) as a zero-frequency > > (co)sine: > > > cos(0 * n) , > > > where n is the sample number. It's constant, its value doesn't change, so > > the frequency of its changes (oscillations) is zero. > > > As you look at discrete sines with an increasing frequency, you would get > > a signal that switches from +1 to -1 going through zero (+1, 0, -1, 0, > > +1, 0 and so on), which is really: > > > cos(pi/2 * n) , > > > where n is the sample number. So, it's a (co)sine signal with the angular > > frequency of pi/2. This means its "physical", temporal frequency is a > > quarter of the sampling frequency (2*pi / 4 = pi/2, where 2*pi > > corresponds to the sampling frequency). > > > The most rapidly changing discrete signal is +1, -1, +1, -1 and so on -- > > switching from the most positive value to the most negative value (and > > back) every one sample. This is really: > > > cos(pi * n) , > > > which means a half of the sampling frequency. This is the Nyquist > > frequency mentioned in the sampling theorem. You just can't get more > > rapid changes than in a series of alternating +/-1, or more generally, +/- > > amplitude. > > > Now for more complicated signals, it's usually a matter of applying a > > Discrete Fourier Transform to present the signal as a sum of separate > > sine (or more generally, complex exponential) components - quite > > similarly to continuous-time Fourier transforms, which you probably know. > > > Regards, > > -- > > Krzysztof Lubański > > OK. > Thanks for all. > > So; for example we have a picture and an array that represents its RGB > values of pixels. > Can we say how much RGB values of pixels are irrelevant it has a high > digital frequency and vice versa.Are there 2 different digital frequency concept? 1-) In DSP books, they say: omega = 2Pi*(fa/fs) Here, there is a sampling so digital frequency is related with time and sampling ratio. 2-)In image processing: Frequency is about pixels values. How fast values are changed. For example: High frequency: 0 255 0 255 0 255 0 255 255 0 255 0 255 0 255 0 0 255 0 255 0 255 0 255 255 0 255 0 255 0 255 0 0 255 0 255 0 255 0 255 255 0 255 0 255 0 255 0 Low frequency: 255 255 255 255 255 255 255 255 255 255 255 255 Here, there is no time relation. But in first expression analog frequency is involved. I am confused.
Reply by ●August 25, 20092009-08-25
>On 25 A=C4=9Fustos, 12:34, rotor cli <rotor...@gmail.com> wrote: > >Are there 2 different digital frequency concept? > >1-) In DSP books, they say: >omega =3D 2Pi*(fa/fs) >Here, there is a sampling so digital frequency is related with time >and sampling ratio. > >2-)In image processing: >Frequency is about pixels values. How fast values are changed. For >example: >High frequency: >0 255 0 255 0 255 0 255 >255 0 255 0 255 0 255 0 >0 255 0 255 0 255 0 255 >255 0 255 0 255 0 255 0 >0 255 0 255 0 255 0 255 >255 0 255 0 255 0 255 0 > >Low frequency: >255 255 255 255 >255 255 255 255 >255 255 255 255 > >Here, there is no time relation. But in first expression analog >frequency is involved. > >I am confused. >There's a thing called "spatial frequency". The analogy is roughly wavenumber (m^(-1)) is to frequency (s^(-1)=Hz) as wavelength (m) is to period (s). Or you could use pixels instead of meters. It's all the same idea, so the two cases really only differ in physical interpretation (and 1d vs 2d). Moreover, your image is still sampled into pixels: try resizing both of those images (add more pixels for this experiment. If you take pixels away, you'll alias in this case). You are looking at high and low frequency as relative concepts, compared to one another, or compared to the Nyquist rate...either way. In the former case, you would still call those "high" and "low", but in the latter case (compared to Nyquist after doubling the image size), you might call them "medium" and "low".
Reply by ●August 25, 20092009-08-25
On 25 Ağustos, 16:04, "Michael Plante" <michael.pla...@gmail.com> wrote:> >On 25 A=C4=9Fustos, 12:34, rotor cli <rotor...@gmail.com> wrote: > > >Are there 2 different digital frequency concept? > > >1-) In DSP books, they say: > >omega =3D 2Pi*(fa/fs) > >Here, there is a sampling so digital frequency is related with time > >and sampling ratio. > > >2-)In image processing: > >Frequency is about pixels values. How fast values are changed. For > >example: > >High frequency: > >0 255 0 255 0 255 0 255 > >255 0 255 0 255 0 255 0 > >0 255 0 255 0 255 0 255 > >255 0 255 0 255 0 255 0 > >0 255 0 255 0 255 0 255 > >255 0 255 0 255 0 255 0 > > >Low frequency: > >255 255 255 255 > >255 255 255 255 > >255 255 255 255 > > >Here, there is no time relation. But in first expression analog > >frequency is involved. > > >I am confused. > > There's a thing called "spatial frequency". The analogy is roughly > wavenumber (m^(-1)) is to frequency (s^(-1)=Hz) as wavelength (m) is to > period (s). Or you could use pixels instead of meters. It's all the same > idea, so the two cases really only differ in physical interpretation (and > 1d vs 2d). > > Moreover, your image is still sampled into pixels: try resizing both of > those images (add more pixels for this experiment. If you take pixels > away, you'll alias in this case). You are looking at high and low > frequency as relative concepts, compared to one another, or compared to the > Nyquist rate...either way. In the former case, you would still call those > "high" and "low", but in the latter case (compared to Nyquist after > doubling the image size), you might call them "medium" and "low".Hmm. For you first paragraph: Can you please make the analogy for fa and fs with pixels. For "spatial domain".. I mean how can fa and fs be related wit pixel example. fa = pixel count? or fs = pixel count? or something else? For second paragraph: Books say: high frequencies are around pi and low frequencies are around 0or(2Pi) in frequency domain. What is that mean? Yes, (as Nyquist)if fa = x and fs = 2x then 2Pi*(fa/fs) = pi. OK. But if we increase sample ratio then pi increases, so why do books say low frequencies are around 2Pi? It is really hard to understand what DSP books are talking about....
