Those sidelobes are the result of the limited resolution of the data from the DSO, along with the fact that the sampling in the DSO is not precisely synchronized to the DDS output waveform, which results in a tiny amount of apparent (not actual) amplitude modulation of the actual waveform.
If you oversample and apply a proper sin(x)/x reconstruction filter to your DSO data, those sidelobes will disappear.
In most of the cases,the Fourier transform of a signal is symmetric about positive and negative axis. So i think the computational complexity increases. Also, energy on negative side unnecessarily gets calculated/wasted.
For real-valued signals, the Fourier transform is conjugate-symmetric about the y-axis.
However, it's entirely possible to use this information when calculating the transform (or estimating it numerically) and so there's no increase in computational complexity.
In signal processing, complex-valued signals are also considered, and when these are used then the transform is no longer conjugate-symmetric.
In the Fourier transform formula the limits of integration are from -infinity to +infinity .But for a signal which is continuously or exponentially increasing,one can't compute it's Fourier transform.
Yes. This is essentially why the Laplace transform exists.
My experience, however, is that the Laplace transform is rarely needed for practical engineering work (at least in my area of experties).
After computation of Fourier transform of a signal, we get Phase and Frequency spectrum of the whole signal which is localised in frequency domain only . But from both these spectrums,we don't get any spatial component features.
I'm not sure what you mean by this.
In image processing, they certainly do do Fourier transforms between the spatial domain and the spatial-frequency domain.
If we think practically, concept of negative frequency doesn't exists.
Negative frequency exists if you consider complex-valued functions and use the complex exponentials \$e^{j\omega{}t}\$ as your basis set. This allows you to keep track of in-phase and quadrature components without doing separate sine and cosine transforms.
As mentioned above, practical Fourier transform calculations take advantage of symmetry and don't do any extra work to determine the negative-frequency components.
Best Answer
You state you've not done any windowing, even if you have, you'd still expect a large DC signal (from the vertical offset of the trace), which will have leaked into other low frequency bins.
The FFT takes a signal which is a loop (ie it repeats over and over again). If your signal doesn't match at the ends, you get frequency components that correspond to harmonics of the period of the loop. There are various techniques for helping fix this, such as windowing, zero padding and pre-whitening.
If you're genuinely getting a signal at that frequency (eg most things have 50 or 60Hz components from AC), you can remove it, by filtering, either in the time domain before the FFT (using a FIR or IIR), or afterwards in the frequency domain after the FFT.