# Confusion in AC and DC signals

I have certain doubts in the fundamentals of AC and DC signals.

Most of the time, we deal with DC signals in the form of batteries, whose waveform is a constant signal with peak as 1.5v

However, i came across some resources, that told certain other signals are DC as well. For your reference, i have enclosed the resources and the respective waveforms here.

Figure 2, Please ignore the "bidirectional" word on the image. So, are these signals AC, or DC? Both the sources have mentioned that they are DC signals (well, the first one is apparently "DC Pulsating" and the second one is a "DC time-varying". This confused me, and i wanted some better clarification and knowledge on these. From what i observe,

1) Any signal that is above or below the time axis (i.e the same polarity all the time) can be called DC?

2) If i have an AC signal, say a sinusoid, and by appropriately DC shifting it above / below the time axis, can i make it a DC signal, if the above point is true?

I would seek your expertise and your insights on these images as well, and tell me why these signals are DC.

Thank you.

The signal in question is a rectified sine-wave. This signal has a non-zero average, i.e. a DC component. It also has AC components at f, 3f, 5f, etc. where f is the frequency of the non-rectified signal.

• Thank you sir. That's what even i thought. However my doubt is, can we safely say that the signal (Figure 1) is a DC PULSATING signal? Many people say that the output of a rectifier is DC. Is this what they mean? DC Pulsating signal Also, what are your opinions on the second figure? – Nishanth Rao Jul 6 '19 at 16:17
• I'm not sure what people mean usually by DC Pulsating signal, but for me it would be a rectangle wave with a duty cycle between 0 and 100%. – Ben Jul 6 '19 at 16:19
• It's common vocabulary to call a signal that is only positive a "DC signal", even if not constant. To be more rigorous you could say there is DC component on which is added an AC component. The AC component can be described in many way :frequency/thd, spectral content, etc. I have never heard the term "DC pulsating" signal – Pier-Yves Lessard Jul 6 '19 at 16:45

When you have a continuous-time periodic signal, you should use CTFS (continuous-time Fourier series) to determine whether the signal is DC, AC or a mixture (AC + DC).

Given the periodic signal $$x(t) \neq 0$$, perform a CTFS analysis; $$x(t) \longleftrightarrow a_k$$ :

• if $$a_0 \neq 0$$, but all remaning $$a_k = 0$$ for $$k = \pm1,\pm2,...$$ then it's a pure DC signal

• else if $$a_0 = 0$$ but at least one (two) remaning $$a_k \neq 0$$ then that's a pure AC signal

• else if $$a_0 \neq 0$$ and at least one (two) $$a_k \neq 0$$ then it's a mixture signal having both a DC value and AC part.

• That's exactly what I thought initially sir. But the value $$a_{o}$$ gives the Average DC / DC component of a signal. So if the above signals are DC (just in case) then the Fourier coefficient $$a_{o}$$ would just give the average value of those signals mentioned. So you are assuming that DC signals are the ones which donot vary with time, and that all the above signals are mixture of both? – Nishanth Rao Jul 7 '19 at 0:40
• yes that's what I assumed. All of the above signals are mixtures (with DC and AC parts) – Fat32 Jul 8 '19 at 1:26
• Thank you so much for your insight – Nishanth Rao Jul 8 '19 at 5:50

Actually AC and DC are terms that come from descriptions of types of electrical supply currents. There is an interesting history between Tesla and Edison on this, you can look it up. AC stands for alternating current, in signal processing terms it is ideally a pure sinusoid. DC stands for direct current, ideally rock steady. The terms have been co-opted by signal processing, where DC generally means the long term average of a signal, and AC refers to any fluctuation around that. There is no problem adding them together, so any signal can be decomposed into its DC and AC components. Generally, this simply means substracting the average value of the signal out to yield the AC portion. There's really nothing more to it than that. Personally, I only use the DC term in signal processing, and that is simply because it is a well known name for the DFT bin with an index of zero (one in MATLAB).

Another name for a DC offset in electronics is a bias voltage. Mixing terminology from different fields is bound to cause some confusion. Yes, your output does look like is a bridge rectified AC current, so technically it is neither AC nor DC in electronics, but in signal processing it is a mix of AC and DC. Go figure.

Okay, so I looked it up.

https://en.wikipedia.org/wiki/Direct_current

It disagrees slightly with my understanding. I'd go with it.