Batteries are expensive! Well, not really. A good quality battery isn't that expensive when you consider what we spend on our music gear. When you put a cheap battery in your instrument, you may not be seeing it's full potential.
For example, we had a Taylor acoustic guitar come in for work. It was being used nightly to perform with Cirque Du Soleil on tour. The sound guy was complaining of the Taylor ES system being noisy. He could hear it through his headphones and nobody could figure out what the problem was. When I opened it up to see what's going on, I found a rechargeable 9 volt battery. Upon closer inspection, the battery was actually rated well under the required 9 volts. I swapped in a Duracell alkaline 9V, and the problem was solved.
These pickup systems, pedals, wireless units, etc... that are built to operate on 9 volts are expecting to see a proper battery. If the battery is weak, the quality degrades. You get symptoms such as noise, distortion, or failure.
You can find studies that have been done to show which batteries hold up over the long term. The basic big name brands like Duracell and Energizer are excellent choices. Usually anything that says "Heavy Duty" or the like is not heavy duty at all. These batteries die quickly and sound quality dies with them. Anything from the dollar store or discount bricks of batteries are fine for toys... but not for professional instruments. Spend the extra couple of bucks.
If you have a multimeter, check your battery's DC Voltage output. A good one will read a little higher than the rated voltage. If it reads a little under, then it's on the way out. I consider anything less than 9V to be a throwaway.